I will admit, technically I dont understand what you propose. (details)
But questions is, what problem are you trying to solve?
energy? You cant save energy when it is proof of work.
But you can try to do something like the other proof schemes and puzzles which try to be bound by memory size and the like. My proposal is quite the same, but is based on password hashing and trying to stop the chain.
Lets assume, somehow we come to agree to make Bitcoin HARDER (you know, lets burn some fuel) to solve. Lets say, we will somehow make it 10 times harder to solve.
Do you know what will happen? Bitcoin network will just ADJUST itself back where it was. (10 minute mark) It does not MAKE ANY difference.
Block time and difficulty should be no problem. I think they would adjust like the difficulty target would do with a falling hashrate.
You are making a change, which will not make ANY difference. Right?
I believe it would make a difference. The physical work is power over time. For the time where the additional input to the block is unknown, the usual proof work cannot be done. So energy is saved.
I think the drawbacks are: 1) It increases the likelihood of a 51% attack, which could be mitigated by creating the fastest possible hashing hardware. 2) It makes validating the block-chain slower for the end-user. Benefits: 1) Some energy saving.