I also played family accountant for several years, but it was quite difficult when the other player was hiding, stealing, and lying. I admire you for tackling this difficult portion head on; most people prefer to bury their heads in the sand and pretend that there is no problem, even when the debt collectors start harassing them.
In the end though, what do you think will come of budgeting with him? IMO, he'll find ways to finance his addiction, and you'll end up policing this whole thing, which you shouldn't have to do.
ITA with Thumper; it's time to separate the finances and start looking at how you can protect yourself from this person.