I still think the best DW/ST crossover would be Tom Baker's Doc meeting Kirk's crew. Lots of larger than life characters all round there, while I think Baker and Nimoy would have meshed well. While he and Shatner could have competed in the overacting stakes ...
You know the 4th Doctor (well sort of) did appear in a TOS novel for like a few seconds. I believe it was My Enemy, My Ally.