For the 8x8 table there's a trick you can do which I suspect the heuristics never considers (because the rule violation is not 1 but many steps away): if you have a chit of one color on 1, 5 and one more above 5 then any more above 5 can't be of this color otherwise 2-4 all three would need to be of the opposite color and that's illegal.

Same for 1,2,4: 5 is of the opposite color otherwise 6-8 are of one color.