Be careful. These boatmen will sleep with your women and there will be an altercation deep inside the earth. If you think that you're ready to handle that, read on, but be aware it's likely to happen.
You're going about this the right way, painless private and your equipment will be dialed, boatmen get to row the rapids and get on a permit, everybody wins. But you need to offer something to the real deal river runners that have will make this happen for you, at a fraction of the cost of a commercial trip - which is what your group is best suited for.
My advice is to dump one of the trips, take the few people that you really want to share the experience with, and put a recruited boatman in charge of each raft. They get all the rapids and don't cook or do dishes. That's a hell of an equitable arrangement if you ask me. When these guys and girls show you the time of your life, day after day, it will seem like a good deal for everybody. They might even bring a firepan, a stove, or a raft and save you a chunk of money.
The point is, there's a lottery system now and trips are pretty easy to get on for the experienced boatman. $12-1300 is also a big chunk of money for the experienced boatman, who may be accustomed to putting together trips with communal gear and food shopping. But to be cooked for for 3 weeks.... it would be worth the price tag, and worth the company, because let's face it - you are not their ideal boating partners and the camaraderie is everything down there.
I hope this is useful advice, but I've talked to friends on the guide side of arrangements like this after Grand Canyon trips and it might be useful to remember what these people sacrifice to take you on the river.