Good question.. Since you don't really have the input(s), I think it's
fine to always assume sufficient time/height on CLTV/CSV checks.

In this general signing-a-script context, I think a verifier might want to see the time conditions under which it may be spent. The proof container could include an optional nLockTime which defaults to 0 and nSequence which defaults to 0xFFFF...

I think it would just use the default (SIGHASH_ALL?) for simplicity.
Is there a good reason to tweak it?

I took another look and there should definitely be a byte appended to the end of the sig so that the encoding checks pass, but I think it might as well be a 0x00 byte since it's not actually a sighash flag.