Hash the folded protein with the previous POW. Problem solved, no?

(I think the important thing is that you have to prove you didn't start the current pow until the previous work unit is done, right? Fortunately, there are lots of proteins to be folded. You can use the previous pow to select the parameters for the next pow. The hashes are uniformly distributed, so that will eventually range over the set of proteins.)

Not at all. What's stopping me from hashing the result with something else? The base of the work must be in changeable. That's the whole point of POW in this case. If you want to rewrite history you need to do the POW again, in your system that doesn't need to happen.