I would say the best way to keep the cost down is to keep the animosity to a minimum. I know that's easier said than done when dealing with an alcoholic, but really, the more two people are out to "punish" each other, the higher the cost. The estimate I got was minimum of $12,000. I worked with my XAH and compromised a lot and we did it without lawyers. It ended up costing me around a thousand dollars. I was lucky that he did not fight me. There were times when I thought he would, but in true alcoholic form, he was all talk and no action.
Shop around, explore your options, and see if you can come to an agreement. It doesn't hurt to try.
L