I think the idea is an interesting one. I think it could likely work. However, the benefits are limited. Yes, you'd save some electricity, but as has been previously mentioned, miners will always be willing to spend up to the amount of the block rewards in order to mine blocks. So this wouldn't save money, because miners would buy enough extra mining equipment to offset the cost they would be spending on electricity. It would also mean that miners would use their ASICS for something else the rest of the time, if possible, which might mean that electricity isn't actually saved. In order to actually save electricity, the PoW algorithm would need to be designed such that the ASICS could not be used for other things (not sure how possible that is).
The mining scheme should be workable tho. Let me recount the way I would do this:
1. At the beginning of each retargetting period, the first block mined is basically the starting gun,
2. then everyone mines a receipt on top of that block at greatly reduced difficulty (1/2016th the difficulty) for 10 minutes,
3. as soon as anyone collects 2016 receipts (adding up to a full normal block of work) they put those receipts into a block and hash that until its been mined at the normal difficulty. This step should exist so the race continues, rather than having a point of failure of the miner that mined the first block in the retargetting period (what if they refuse to sign and broadcast a list?). Also, this ensures that its difficult to create a different list of receipts.
4. once the step 3 block has been mined, it locks in the receipts, and therefore the order of the next 2016 blocks
5. The miner who owns the first receipt in the list must include the hash of the commitment block containing that list as its previous block.
6. For each of the next 2015 blocks, the miner will basically have a time limit to mine their block (rather than racing). If they create their block within the time limit, they get to create that block. If they miss their window, the next miner in the lineup can broadcast their block on top of whatever the most recent block is.
While in normal PoW, miners are racing to mine and broadcast as fast as possible. In the pre-ordered block creation, miners actually have an incentive to wait until their time is almost up to broadcast their block, because they want to include the highest-value transactions they can (and they want as many mempool options as possible before committing to a block). However, because the next miner can skip them if they miss their window, they also have an incentive to broadcast their block well enough before their window ends that they don't risk being skipped. So miners would probably wait until say 10 seconds before their window ends to broadcast their block, but if the previous miner missed their window, they would probably broadcast ASAP (at the beginning of their window) to capture the transactions that miner missed.
An interesting thought experiment is: what should honest miners do when they see conflicting chains? Like, lets say one chain has block receipt 300 skipped but contains a block for receipt 301 and the other chain doesn't have 300 skipped but doesn't contain block 301? Which chain should that miner choose? I suppose this would be like any orphan situation where the miner would choose the chain they saw first, since they're both the same length. Maybe there isn't a problem here.
In any case, this is an interesting idea and was fun to think about. But I don't think the benefits are enough to make it worth the effort and risk of other issues.