Thanks again! I think I managed to bypass the issue. Fin supports are generated for each edge separately, so there's some overlapping geometry. It appears that Chitubox had some issues with too many coplanar triangles overlapping at the same time. I've added some tiny amount of noise to fin base positions, just to move the triangles enough so that Chitubox doesn't break when slicing the dice. Rotating the dice (like by 1 degree) in fin support settings prior to export seems to fix the problem as well.
I'll try fixing the issue properly (that is, generating continous geometry instead of overlapping per-edge fins) when I'll have some more time to do so, this is all I could do right now :x