PoW and green won't go.
Giving people a lower chance to gain a reward overall makes things greener but also harms the security of the chain.
PoM as you call it is probably similar to what has been attempted with proof of storage/proof of space - I'm not sure how that worked except storing "plots" over a drive. (since you can mount ram as an ssd then it's probably a similar thing).
Yes; in general, the conclusion is usually:
(a) You created a good system, but it's just abstracted PoW so there won't be any 'greenliness benefit' compared to 'traditional PoW'.
(b) You created a bad system, such as PoS.
Is it an underrated concept to make the PoW more "green"?
I'd say it's wrong approach to make PoW more "green". It's more realsitic to convince miner to use renewable energy and dispose broken mining hardware properly.
You could also add that making mining less energy hungry would erase the current incentives in Bitcoin mining that motivate mining operators to go out of their way to harvest every last bit of otherwise wasted energy (since it's so cheap). Meaning less energy hungry mining schemes could potentially have little impact on the amount of energy that is (uncleanly) created, which is what ultimately matters. Like, if we have nobody who builds mining facilities near hydro plants and uses the excess energy at night, or operators buying up solar energy at noon, when nobody uses their lights, but energy production is highest, that energy will still be produced and simply go to waste.
