Wasn't the entire point of picking SHA-256 to both check the integrity of the existing ledger (why it's a hash) AND as a proof of work lottery? The "problem" being that instead of being a proof of actual work, shortcuts in the work were found. It seems then that a good solution would be to force many different types of proof of work. Different basis of hashes are obvious, but maybe some type of actual work every so o…
This would create many more opportunities for finding shortcuts like ASCIBOOST. Some of them might be much worse.