Or “pursue and persist”.

“Cease and desist” has nice assonance, I feel “pursue and persist” matches a little more in that regard, though both are decent.

As regards meaning, “proceed” and “pursue” are both good, taking slightly different angles but to essentially the same purpose.

Maybe, but ‘continue’ is a better negation of ‘cease’. Proceed can mean (usually means?) to do something one has not yet started, rather than to not cease.