More on suicide checkers draws

I'm just back from my easter holiday in Saas Fee, where I tried to avoid serious injuries while sliding down snowy mountains on skis. I tried thinking about how to solve the suicide checkers problem, but I couldn't find an answer. The problem is this: In general, so I am told, material is quite important in suicide checkers. The side with more material is generally well off. However, unfortunately, there are many draws like those mentioned in the last post. These fortresses are of course detected by the endgame database, but only for positions with few enough stones. Of course I could compute larger endgame databases, but the problem remains: I cannot trust the verdict of Suicidal Cake, unless it sees a database win/draw/loss, because Suicidal Cake believes (like a regular checkers program) that being up a man or two is going to win a game. If you have any ideas on how to score suicide checkers positions more accurately, then drop a line here!