You get reset to 3 shards, I did say that. But it's still better to try and get 2xDB in before the shard reset as each cast gives you another chance of a DC proc, and that's why you do it, not shard generation (plus its free - admittedly rubbish - damage) - getting that DC proc to combine with the first HoG hugely smoothes out the opener though.
Synergy will be up 99.9% of the time as you do your set-up, but I've generally found it expires pretty often before the first TKC cast if you're maximising that 12s window from your first summon. That's a huge loss in terms of the size of your TKC hit (approximately 25% bigger with synergy). If you are tracking this (and you should be), you should shorten the opener by a couple of DBs, generate fewer imps and throw out a slightly smaller TKC to benefit from the damage buff over prioritising imp generation. After that it's just RNG, you can't control the synergy proc, so you've no way of making it fire off when you want it to, and I'd certainly not advocate throwing away a good TKC set-up because it didn't proc, as you've no way of knowing whether it will any time soon. However, as I demonstrated, with the maths, you're better shortening your TKC set-up by as much as a 4-shard HoG. A TKC with 4+ imps (including Imp DS ones) and 2 DS with synergy is better than 10 imps and 2 DS without it.
As for the opener... I prefer to throw DS with the first HoG always (without a proc) because while you should get a proc while building up your shards when you don't get a proc after the DBx3, and you end up with a crappy HoG for 2 it becomes a horrible mess.
But aside from personal preference, there's multiple good reasons why it's better to throw DS alongside the first HoG - it empowers your DB by an extra 60% (w/o proc, 80% with it), it gives you the freedom to tailor your second HoG to the synergy window if it doesn't refresh, and every single guide and piece of advice you'll find tells you Call DS is one of your highest priority abilities and should be used on CD. Why would you willingly and deliberately delay casting it by up to 5 casts?
Lastly, by sticking it in the back of your opener, you're ensuring that you're casting it around the 15-20s mark into a fight. There's some other issues with this... firstly, you're not going to be casting your second set of DS until the end of the heroism that's popped on pull on most fights. So you're not getting the full TW haste benefit on your second set of DS. Secondly, mechanics have started - that might mean different things on different fights... On Elerethe, the boss jumps away, and while your imps can still hit her, I'd bet your DS, being melee attacks, can't (can't be bothered to check logs and confirm it), so that cast is largely wasted. Or it might mean you have to move - losing a DB cast is less painful when the important part of your TKC is set up and waiting and you're not fishing for a DC proc. Thirdly, if for some reason you need to shorten the rotation - because of movement, mechanics or synergy - you have the option to shorten the rotation by shifting the DE out and going DB(s) - HoG - TKC - DE, rather than dropping DBs and going straight to HoG-DE-TKC and losing an imp. It's minor, but empowering imps adds around 7k to your TKC, where a baseline imp adds 31k to your TKC. As such having a 4 unempowered imps is better than having 3 empowered ones. Failing to empower DS and any imps you got with Imp DS is a much bigger loss though, so that becomes, not undroppable, but sub-optimal to drop.
I also stand by what I said about fixing the opener, there's nothing fundamentally wrong with that rotation (even the Call DS at the end is a matter of preference, I think it's sub-optimal for the reasons above, but I'd be willing to bet it's a marginal difference in real damage terms), but you're so dependent on haste and whether or not there's a TW. You can't just say 'do this'. You have to say more like - use this as a guide, find where your breakpoint is for your level of haste with / without TW and extend / shorten it as necessary.
While the point about new players is taken, Demonology is not a simple spec (imo it's actually one of the hardest to play really well), and the initial guide or Icy Veins covers enough for casual players. By page 50 of the forum, you're not really talking to people who want to play casually. The playstyle requires a lot of micro-optimisation to maximise output and it's better to get in the habit of doing it right and understanding why you should do it a certain way than do it a way which works fine most of the time.