+1 on getting off the mortgage/deed of the house and having everything tidied away with no strings left to tie you two together. That includes, if you are going to support him with the remaining costs for the kids, that you pay school stuff directly, and if necessary, transfer X amount of money to him monthly for groceries and other support. X being, of course, a set amount that you work out between you and/or what the state dictates, not, "Oh, we had to do a big re-stock this month, so I need a bit more money."
I don't personally have experience with this, but I did journey very closely with one friend going through a similar situation years ago. She, like you, was willing to settle for a little bit less than she was entitled to, in order to make things easy. (In her case, she took responsibility for all the debt, mostly incurred by his gambling, and left him with the car that she had paid for - she knew he would default on the debt and leave her with it anyway so it gave her peace of mind to just know what she needed to do, and she also knew he couldn't keep his job without the car and she loved him enough not to want to leave him with no means to support himself.) It's your choice, what you would rather do - walk away with less, but not have to deal with the hassle and the potential damage to the relationship? Or get at least some of what you're entitled to, to better secure your financial future.
Two thoughts, if you do decide to push for more than what you've outlined:
1. If the primary retirement plan for you both was to live off his pension/401K (I'm Canadian, I don't know your terms!) then you should absolutely be entitled to part of it and part of any equity in your matrimonial home.
2. You are not "forcing the sale" of the home, though it's possible that his financial situation will force the sale of the home. In other words, you're happy to see him re-finance the house to buy you out (or even, if you decide you just want to be done with it easily) to carry the whole mortgage. But if he can't qualify to do so, then you still need to be off the mortgage/deed, his limited resources not-withstanding. He can choose what he does with that information - maybe he could get a friend or international student or someone to move in and share the costs? Or find a way to boost his income to qualify on his own? Or maybe he'd have to sell. But that would be the bank's financing requirements fault, not yours.
I know that I haven't really answered your question about cheap processes for getting the divorce done, but I just had to weigh in about that other stuff. I wish you luck with all this, and hope that things look up for you in the future!