I have only looked at 28 of the recommendations (because I am 28/36 and I refuse to look at guides before beating the respective artifact challenge, because where is the fun and accomplishment for me in that?), and I must say that I have far less objections to the guide in its current state as compared to when I saw it the first time.
Also note that I did most of these challenges (except Havoc) months before the recent artifact power boost so my opinions or views may not be accurate either.
Let's start with the healers; although the wording on AoE-spells has greatly changed, I still disagree with it in general. The main thing is to not use any spell where they are not efficient heals, which is a good one, but if you need to use them often enough that you start having mana troubles, this is never an issue.
For instance, Monks definitely have good usage of Essence Font. If you are behind on multiple targets, using Essence Font is brilliant - otherwise you will have difficulties using your globals anyway. Why is Essence Font so good? The healing itself.. could be better. The buff it leavese on the target is fantastic, however. You have double mastery-triggers on targets. Meaning that (if you have a mastery-heavy gear set which you should unless you are a raider) your Effuses heal for 33-40% more on all targets, without having to apply Enveloping to them. Mastery heals more than the actual Effuse (in mastery gear).
Shaman, you definitely should spend time on Chain Heal if it is effective enough on at least 3 targets. You also get Tidal Waves from it. I avoided Healing Surge as much as possible (obviously), so being able to have powered up Healing Waves saved me as much mana as compared to what I would have spent on individual Healing Surges in that time. You also listed Drums of the Mountains for Shaman, which I must think is a mistake since the class has built-in Bloodlust. I also don't recommend popping it that early since it was certainly not needed. All it did was make it more difficult for me to heal since I needed to spend more time healing the buffed-up party members - I saved BL until... stage 7? I needed all the DPS help against the boss as I could. Ancestral Vigor has never impressed me as a talent, and it didn't in this encounter either. Earthen Shield totem helped a lot on cooldown, especially during knife dance et al.
I would also recommend far more spells on mouseover-macros as I can't see any benefit from not having them - why would I ever need to have a party member targetted? (no real input on the other targets)
Xylem:
This can be extremely random.
My Frost DK (again without looking at guides and with like 910 gear and 880 weapons) managed to one-shot this encounter even though I forgot to spec out of my PVP talents. Without consumables.
My Arms Warrior needed 6 attempts, and two of those deaths was trying to Leap out of ice shards (before I started Cleave->WW them instead). Once I got over that, I got confused about arcane phase twice, and I failed Stage 2 once.
My Havoc Demon Hunter needed 3 months and 386 attempts (where at least 40 of them was post-artifact power buff). It is simply impossibly random. The strategy that gave me the most consistency was using KJ-trinket and Artifact Weapon alternately on the Ice shards, not picking up as many orbs as I could, so I could save them for multiple Eye Beams for each frost bolt phases (and also healing). Arcane phase randomly failed several hundred times for me because the mirror images were casting out of synch and kept slowing and pushbacking me.
Several times my interrupt went off but he kept casting. I think I got to phase 2 four times total during these 386 attempts, and downed him on the fourth one. So I can't really offer any opinion on the tactics of Havoc :P By far the most difficult artifact challenge I've done (and by contrast, I two-shotted Vengeance). I did find Fel Eruption crucial in P1 though (boss is stunnable), enough so that I forewent Nemesis for P2.
Survival, I had issues before I realised you had to Flare. That took me three failed arcane phases of literally standing on top of him. The issue with doing things guideless. :P Those three failed attempts were great otherwise, since it helped me learn Survival, a spec I had never played before and I got to phase 2 immediately after (and had to try and sort out slows and failed) and killed it the attempt after. Without relics in the weapon.
I also realised here that my Nether Ray's debuff on Bloodlust-equivalent didn't reset between attempts so I had to lag behind with the DPS intentionally to be able to have a fresh BL for Phase 2. Another note here is to NOT have Growl on auto-cast on your Bloodlust pet here..
This is just me complaining about how incredibly random Xylem can be and not critique against the guide.
Tank:
I strongly disagree with the rankings on these. Phase 1 is incredibly trivial for Warrior (I sometimes went through it without even getting an infernal, when I erroneously thought I needed to burst through in p1, having nothing left for Kruul :P).
I admittedly have 2p tier-bonus (normal version) on my warrior, the only character with this luxury, but rage is simply not a concern at all in p1 - Battle Cry has a 20 sec CD with Anger Management! At most. I imagine it is even more ridiculous now post-artifact power boost.
I personally detest both Storm Bolt and Shockwave, since Warbringer is infinitely better in all content where you can effectively use it. It deals the most damage, it has the least cooldown and it doesn't share DR with anything, even itself. It is super easy to use (mouse-over macro) and you are even given Friendly targets to Intercept in Melee range with it.
I preferred Renewed Fury over Avatar since it has a 100% uptime.
p2 was where I struggled. Since I do this guideless, I didn't know you could reflect the debuff and the orbs didn't clear the debuff with Pal or Warr (did on the others) and sometimes the draggy-lines pushed you off interrupt range. This should be trivial as well with Spell Reflection.
Guardian was simple for me, but I literally got Luffa's between attempts on it. The only difficulty was that it was my second artifact challenge whatsoever (feral first) so the difficulty lay in learning the encounter in general. But after Luffa's it was trivial.
Protection Paladin was so ridiculously easy (for me) that I don't see where the struggle lies. The only difficulty for me was learning how it was different to guardian (prot pal was the 3rd MT I got) and I could burst Kruul down easily in just going in twice in his circle. I hear that this is legendary specific, however.
I just used my two normal leggos I always use for Prot (Legs/sephuz) and I didn't struggle the slightest.
Brewmaster was a nightmare, however since there is no healing at all in the class and I don't have any relevant trinkets that can help you. I definitely recommend using Chi Burst for this encounter though, since you can shoot down the eyes with it in one shot. I also had a much better experience with Gift of the Mists than Black Ox Brew. Brews were never an issue with angling Blackout Combo with Keg Smash (although I spent most of my combos on Tiger Palm and hope I got lucky Arti-weapon rolls for dps).
Blood DK was difficult because the DPS was so lacking. The trick was just to whittle him down from outside the circle all game and not spend DRW until you could use it on Kruul, whilst picking up as many adds as possible.
As for Outlaw, I liked it better when you said Blade Flurry was useless. Because it is only worth it to have it active for 2-3 seconds at most, and then those adds are dead. As for the spec of Outlaw, I would recommend Swordmaster in t1 since I very rarely had free GCDs to actually spend with Pistol Shot I much rather get the extra up-front damage and CP from Slash and you swap targets too much for Ghostly Strikes.
Also, if you don't have the healing pants (I did), I would strongly recommend Iron Stomach over Cheat Death, since if Cheat Death ever is relevant in this fight, you are likely too far behind to recover.
Acrobatic Strikes nearly made me able to disregard Fuming Imps however. It is not to be underestimated.
Unholy, I don't see the point of Pestilent Pustules. Epidemic is actually useful in this encounter if you have more adds than you have Defile-CDs. I also preferred Sludge Belcher's 360° "claw" during Dark Transformation and I would imagine Debilitating Infestation to make the mobs harder to round up (different movement speeds depending on affected or not).
Elemental was ridiculously easy; I did it with Elemental Blast so I could chunk an add away almost immediately with it alone. I saved Artifact Weapon for when all of them were together, and Lava Burst or Chain Lightning did quick work of those I didn't EleBlast.
I didn't use any out-door buffs for Agatha (since I didn't know it was possible!), but a buff that you didn't mention anywhere in your guide is Bear Tartare. This speed buff is invaluable in any fight with adds, and I only found it somewhat useless in two of the challenges: Sigryn and the healer one.
Otherwise it really can make or break a challenge. I would not say it alone trivialises anything, but it really is MVP in a lot of them.
Today, I will pick up the Mage Tower challenge at 28/36. Havoc is the only one I've done post-artifact power boost (I really needed it), and the Havoc one was what alone made me take a two-month hiatus from Wow. :P
3xMage, Balance, Resto-D, 2xHoly and Ret left.
And now I also noticed I 'only' have until Wednesday left. I imagine it will go quicker than the 1-2 per week I had previously though..
TL;DR - I make a useless rant with too little recommendations per text committed to the post about my experiences.