I'm personally burnt out from 5+ months of raiding 4-5 nights a week and wouldn't mind the breather also. But I'm prepared to support the majority and continue raiding if necessary. I'm just worried about losing more people to getting burnt out or losing others to boredom and a stall in progression.
From a certain perspective, this is an easy question to answer. You could schedule the runs in Group Calendar or a similar mod ahead of time and only go when the sign-ups are full. Suspend any attendance requirements for the time being so that burned-out people can take a break if they need it, including yourself.
However, there will always be those who feel obligated to attend a scheduled raid, particularly if they know the run hinges on their ability to tank a certain boss or play some other vital role. Also, it can be tricky to communicate which runs are happening and which aren't in time for people to adjust their schedules appropriately.
Still, even with these drawbacks it's one way to approach the situation. But there are other steps you can take also.
The first thing I would do is speak with your raid leader. Ask your RL what he or she would like to do. Your RL is the key to your progression in Wrath, and you want him or her to be happy going into the expansion. So that has to be a large factor in your decision.
The next thing I'd do is poll your raiders. If people are as divided as you say, it may not seem like an effective option. However, you can set up a poll in a way that helps you narrow down your choices a bit. For instance, if you ask people to vote on what they would least like to do, you can eliminate one or two choices off the bat.
Even if the poll resolves nothing, it's a win for you because it shows your membership that the officers are listening to them.
Three other factors are coming into play soon with patch 3.0.2, rumored to drop tomorrow.
The first is obviously the major changes to gameplay, itemization, class abilities, and talents. Everyone will want to try out their shiny new specs, so enthusiasm for raiding will be on the upswing for a little while.
I wouldn't recommend scheduling anything on patch day itself. Server problems can lead to a frustrating night, and it's not uncommon for essential raiding mods to blow up, either. But I can virtually guarantee that you'll have good attendance for a raid a day or two later, no matter what you schedule.
Another factor is the achievement system. Vashj and Kael'thas are both targets of achievements for completing their respective raid zones. So there's a little extra incentive for you to go back and take them down. Although, if you're close to taking out Archimonde or Illidan I guess it's a wash.
Finally, there's the across-the-board nerfing of all raid mobs. It's too soon to judge whether this sweeping change will make the zones easier to complete, or whether it simply makes them possible to complete with the changes to potion use and downgrading of key abilities like Lifebloom.
One thing is pretty certain, however: you're going to kill stuff faster. That alone might be a breath of fresh air for your raiders on the edge of burnout.
Here's where I weigh in with my personal recommendation. If the patch drops tomorrow, I would ride that wave of freshness and excitement to make a big push during the two weeks after it. Schedule Kael and Vashj runs -- skip as much as you can on those nights and just go straight for them. If you get one down, it'll be a big win for the guild and help improve morale. If you don't, well, you can always blame the changes!
At the same time, keep pushing through Mount Hyjal and Black Temple during those two weeks. Faster clears will mean more time to devote to learning bosses.
Then, at the end of those two weeks, reassess. If you're a step away from downing Illidan, maybe you want to push for another week. If people are just not feeling it, scale back to two nights or so.
No matter what, I suggest that you take a break as a guild for that last week. Maybe schedule one final night for unfinished business. Once Wrath goes live, people will be pushing themselves hard to hit 80 and gear up. If they haven't had that break, they might find themselves burned out before they even start raiding again -- and that goes double for officers!