As I see it you are not having problems with Sartura, you are having problems with healers not paying attention to the world around them. We ran into this problem with some of our healers when encountering C'thun. Healers have to learn to watch bosses and their environment.
Clearing up your screen space is usually a good start. I know a lot of healers that only had about 5% of their screen space not filled with health bars, that needs to change. Better get used to it now then in a month or so. People that die a lot to sartura adds are going to die on twimps trough blizzard and are going to get glared on C'thun.
Remove the emergency Monitor, hide the ressurection Monitor, use smaller more efficient raid windows and you will have a lot more to look at. Seeing stuff will make you aware and thus your healers will be able to react faster.

Learning to use "emergency monitors" effectively will take you a long way. I'm still trying to break about 90% of our guild healer's of the habit of spamming the EMs.
The problem is that everyone wants to heal the #1 guy on the meter - the guy who's most hurt. Which results in him getting spammed with 15,000 HP of heals that he didn't need, while someone else higher up (or a tank) suddenly dies from lack of attention by his assigned healers. And then the priest who is spamming Flash Heal begins to demand innervates, claiming that he's "healing the whole raid and single handedly keeping 40 people alive" and that everyone else is "slacking" because they aren't #1 on the heal meters.

Goes back to what I said before - assign roles. Guys that are assigned to tanks or other critical roles should not be worrying about flash healing the rogue that just ate a chained cleave. A quick HoT here and there is fine, but they should not be concerned with much else. Assign specific people to top off the DPS classes and enforce those roles - call out people who aren't doing their job correctly, especially if their tank dies while they're spamming heals on the EM.

Heal meters are another aspect of working with good raid healing. They can be used to help evaluate performance, sure. But more often then not they're being used to justify someone's ego that they're a "better healer" because they're in the top 10 or top 5 of Effective Healing. Discourage that mindset and that behavior - restrict the posting of such meters if you have to. They can keep a personal meter if they want to see it.. Posting such crap in raid/guild chat just makes everyone work harder at sniping heals and spamming the EM to get higher on the list instead of paying attention to their assigned job.

We've found that 15 healers are becoming way too many lately. Previously before I started arranging healing it was a miracle at times for 15 healers to keep the raid alive in certain fights. Now with careful planning and distribution of healing we consistently find that we've got about 5 healers too many - these guys just tend to sit around with not much to do except backing someone up. So you may find that with good planning you don't need as many healers because you're using the ones you have more effectively - opening more room for DPS (or have those healers do some DPS while waiting to backup someone else).

Two things that might help a lot:
1: Tell your healers to set max camera distance. Some may not even know that they can go beyond the default range (I was really really surprised to find this).
2: Remind them that if they die, their spells don't complete anyway.

Your healers just have to move.

This is one thing our guild does, but I don't feel it's a warm atmosphere friendly for the Priests. The ironic part is that while most class channels in our guild are suffixed with a class (like warrior, mage, etc) the Priest one is appropriately suffixed with "ego". :P

I would suggest having a class team leader and pointing out issues to him/her that you see, rather than calling on anyone directly. I made that mistake before and now I just send a tell to our Priest class leader if I see things that can be improved upon.

Yes, it can be resisted, and yes you can screw up and get more/less mobs than you intended (especially if they're moving fast).

Then for a guild learning Sartura (that would be us) I'd say it's not worth the risk.

There is really no risk.

A Rogue just finds a spot which allows Satura and Co to path around normally, but you can distract them at max range.

1) If one or two resist distract, the mobs just keep moving. A resisted distract doesn't expose the rogue, it just negates the distract effect. Ideally, you want to distract only 1 guard in the front left corner, so a resist is actually a not a bad thing.
2) If you get more than you want, just wait until they loop around again.

Only challenge for the rogue is finishing the right spot, and if they screw up, everybody runs up the tunnel, satura resets and its no big deal.

There is no magic formula for Sartura, indeed (as you say) if your raid doesnt learn how to move and play at the same time they will be seriously struggling at CThun and in Naxx, even the trash before the Twins requires mobility.

Most of the advice you need has already been mentioned. Assign healers to your tank groups, use Hunters on the pull to separate them out and burn down the adds with focussed dps as fast as possible, the fight gets exponentially easier after the adds are down. Make sure your Druids are using HoT and Swiftmend as these can be cast on the move - often a life-saver.

Once you have Sartura alone the melee just need to learn the rhythm of whirlwinding so that they avoid as much damage as possible while the tanks try to keep Sartura relatively stable - everyone else surround the boss at max distance, adjusting as the boss moves around.

Update

Okay, so I've been getting a lot of excuses from my raiders about spot healing and the like. I keep hearing from them that druids cannot spot heal. I'm under the impression, that spot healing isn't so much class restricted, as it is player restricted.

Do you guys have any tips / ideas / words of advice upon this?

Which classes should make good spot healers? Which don't? Should I try and encourage my healers to break out of their shells and learn how to manage spot healing? Or should I just cater to their strengths and submit to their wishes?

What do you mean by spot healing? If you mean topping dps off and throwing small fast heals to bring people to full, druids are not the best at this. Our heals are slow, and almost always a flash heal or flash of light/lhw will beat us. Its frustrating to have all your heals sniped. Druids can keep a group up perfectly fine, but the faster healers need to give them that extra .5 seconds to let their heals land/hot to tick. If they won't do that then the druids lose a lot of their value in the raid.

Are your druids ranking down? Rank4/Rank5 Healing touch is more than adequate for spot heals (rank4 being the better as it is faster, but if it does not yet heal for 900+ is not really useful yet.)

If you have some Preists/Shamans blowing full mana pools topping off other peoples groups all the time you have a problem. Healing needs to be spread between healers and if you have a terribly agressive healer he may be causing your other healers to either slack off or just give up. (Bob will get it. Why even try he beats me every time...) Find out if that's the case and if it is tell that guy he needs to share the heals a little bit, because he is probably and aggro magnet or a pot burner and most likely not even happy with his own performance (as it is costly and he dies often.)