I don't believe your proposal reduces energy consumption. Energy consumption in PoW is limited by the value of the block reward, and is not related to the difficulty of the solution. The difficulty maintains the time between blocks.
The goal of the first round is to select the first N2 miners that succeed to resolve the first round PoW puzzle.
How does the network decide which are the
first N
2 solutions? Each miner could insert their solution to their list regardless of how many other solutions they have already received.