I'd like to be able to make a file download request from Stash such that if the file transfer only partially completes, I can make a subsequent request for the file, but only for the bytes that I have not yet received.

I believe one way to achieve this is for Stash to support HTTP byte ranges:

When playing around with interrupted downloads from Stash using curl with the -C (--continue-at) option, I see:
curl: (33) HTTP server doesn't seem to support byte ranges. Cannot resume.