Looks like you are using make with top object if I am correct.
You can use the convert anchor point tool to suck in the bezier handles on the hexagon, that may make it better or worse. Also try object >> flatten tranparency (slide to vector), edit bad points and put a mask on top.
Good question, have never found a perfect solution for this, so interersted in what others have to say.
A limitation in all fitting algorithms - minor differences in segment lengths or simple quantization errors accumulate and then the algorithm needs to do weird things to squeeze one shape into another. In your case I wouldn't bother with this at all, anyway. Seems easy enough to manually split your artwork and turn it into a cube...
A limitation in all fitting algorithms...
Actually, it's more a limitation of Illustrator's belated implementation of Envelopes. Illustrator does not allow you the option of creating an Envelope with its curve handles initially retracted; it insists on always auto-extending them. This "too smart by half" (as Aunt Molly would say) treatment of the feature in Illustrator severely limits its utility.
I've been trying to make that point here ever since Envelopes finally appeared in Illustrator.