you have to find the most efficient signature verification algorithm.

and you really have to construct the canonical form and check the provided ID is correct. this is one of the problems with putting the ID on the wire, it becomes easier to forget.

sorry, but there is no way around this. you can't trust rando relays to do it. even if they do, you can't trust all of them to do it.

for mobile devices, checking an secp256k1 siganature on a sha256 hash of an event is not impossible, and anyway there is now fast libraries for both android and iOS. even, on android devices, you can make a little binary tool that runs to do the job. on iOS, the swift code IS binary so it's just a matter of having the actual function available.