Disney might have deeper pockets than the previous ownership, but they are probably the most aggressive company in existence when it comes to protecting copyrights.

I think the Kirby family was motivated more by the copyrights becoming due in a few years rather than Disney's entry into the picture, or at least I hope so, as picking a fight with Disney just because they are Disney is not a wise move. Their reputation is not to settle, ever, from what I gather. Disney is not likely to throw a few million bucks at the Kirby family just to save themselves some lawyer's fees. They'll grind it out, forever, if necessary.

In the end, I suspect that the Kirbys will not get a dime. While you can make a "moral" case for Kirby deserving a bigger piece of the pie than what he got, the legal grounds just aren't there, in my opinion.