So if I understand this correctly, basically you are suggesting that miners mine for short period of time in order to gain proof that they have one work, which increases their voting power? So it is still just as competitive to win the right to sign, it's just that you can turn off the power every once in a while and coast using just your votes?
Personally, I prefer Burst's method. Do the POWs once, save them to a hard drive, then pull them off in real time and present them as proof that you are holding on to a certain amount of hard drive space used to store these proofs. Seems sort of similar in a sense.
If you're worried about power, it turns out that it only uses ~25% more power than POS but is much more secure due to Proof of Stake issues.
And best part, it's already up and running now!