Not a perfect solution, but some of what you're looking for can be achieved with the Hasher backend:
If you create a hasher remote that wraps a crypt remote, you can essentially use hashes with crypt. Consider setting --hasher-auto-size to a very high value (larger than your largest file) so that it will always recompute hashes on the fly, like local does.
The tradeoff, of course, is that this may use lots of data / storage (calculating a checksum requires downloading the entire file.)