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 I think this might be an acceptable solution. I suppose it cuts the key-space in half though? 
 that was implicit and is mentioned in BIP-340

just keep in mind that as it was, the bit-strength of secp256k1 is about 126 effective bits, and this only shaves off half a bit

the permutations of those bits is an extra factor of two for every bit so it's not a linear relation, losing one bit is really losing 1/126th of the security

the chances of collision are doubled and the time to average brute force is half, yes, but we are talking about a process that would take hundreds of years for one key with all the computers in the world