Resto shamans are weak healers at the moment, if possible I'd replace the resto shaman with a disc priest because they are strong healers and good on fights that you can't 2 heal but don't want to 3 heal (atonement is amazing), they are also great for a lot of fights like heroic horridon, heroic iron qon, and h: jinrokh.
If the resto shaman is good dps it wouldn't be a bad idea to have an elemental shaman - especially one who at least knows how to resto shaman in case a healer misses a raid. If you want to break into heroic modes quickly you need to work for it, as the raid leader (and GM) its your duty to push the guild and raid in the direction you want it to go. If you aren't setting the standards and raising the bar nobody else in your guild will and eventually the best players of your raid will leave for greener pastures.
If you like the idea of raid leading and building a team that can rival some of the best guilds in the world/us then keep working at it, if you want to just be a part of a guild that does well then go find one and app to it and focus on personal growth. I find its much more rewarding having built up a team that is now around world 200 (and continuing to push for better), on only 2-3 nights a week. It is a lot of work, a lot of frustration and you'll face obstacles everywhere you turn but at the end of it all you built it which makes it that much more important.
I would suggest having at least 11 or 12 people on your roster though, so any 1 tank fights you can have the warrior sitting on progression and then bring him in on farm content later to get gear and credit for the kill. The benefits to this are of course not halting all progression because one player misses the raid, having the ability to sub out healers and tanks for a better raid comp, and having every class or multiple specs for raid comp advantages. My roster is currently sitting at 12 people and I am looking to recruit 1 or 2 more people to get it where I want it.
Also, always recruit the player and not the class; the objective is to always bring in someone better than the people you currently have, when you are a new guild or have a struggling roster this might not always be possible but you know you are doing something right when every new person you add makes your raid stronger than it was before instead of just filling an open spot.
I've not properly raided on resto shaman but if you look at the logs there are a few problems that could help them improve. The shaman shouldn't just get a free pass because 'shaman are poor just now'.
The shaman has talented into Unleashed Fury but only cast Unleashed Life 15 times on the Iron Qon kill, a 10min 51sec fight. The spell only has a 15 sec cooldown so should see a lot more usage and is a waste of that last talent point tier. Earth shield uptime was 80%, should this not be higher too?
1 ascendance used, they could've had 3 easily. I dunno how many times healing tide was used but doesn't look like enough total healing for 3 uses either.
It's maybe unfair to analyse the shaman just because they are bottom though. Look at the druid, 80% lifebloom uptime and only 21 swiftmend casts too so it's not just the shaman that could be doing better. Looks like tranquility was only used once too, didn't use barkskin, only used Ironbark twice. It's just easier to look good on meters as a druid since all the hots are fire and forget but I think you'd need to look into more detail than just HPS.
I don't think you quite understand what 3man healing is in fights like these, in fact, in all of ToT. When I say there's nothing to heal, that's an understatement. Why would he use any of these cds when they're simply not needed? To try and ninja heals? He'll lose to the other healers being the class he is.
When I for whatever reason end up 3 healing, the truth of the matter is at some point I tell the others I'm afk for a drink, toilet, or just alttab and they will thank me for it because just maybe they'll have a bit more to do. Even 2man, ToT healing is incredibly boring, with the surprising exception of Dark Animus. Lei Shen can be fun to heal if there's no disc priest, which is like never in our case. (I'm assuming normal modes here which is what I understand is what he's been doing from logs). Today's WoW healing is a lot more of a salvaging role, where even shit tanks should be outhealable, with as result that good tanks take zero damage. Seeing as we have solid players, there's just zip to heal. Our tanks usually sit down for vengeance, that's how much work we have to do. (Obviously this is normal mode, I realize some heroic modes are quite harsh healingwise).
Like I said before and I'll just repeat it, if you want to see what your shaman can do, have him 2man heal. Furthermore, there's been very good advice about bringing it up to everyone. Everyone should be on the same page in terms of expectations. If your healers are a concern, talk to them.