I don't know about the mathematical result (the conditional proof), but I do know that it's easy to expand or limit the edit operations, or change their costs,

I don't know about the mathematical result (the conditional proof), but I do know that it's easy to expand or limit the edit operations, or change their costs, while keeping the dynamic program order the same (so not e.g. allowing 'move this whole phrase' type edits - that would probably be cubic or worse). If you're considering the generalized 'set any costs you like for the operations' problem then you could set the subst cost as 2 and the insert and delete as 1. Again, I know that's not precisely what you asked. I can't think of a reduction from "insert+delete only" problems to "insert+delete+subst" (all operations cost 1) problems (where solving the latter gives you a solution to the former, and the size is no more than k times the original).