I don't believe your proposal reduces energy consumption. Energy consumption in PoW is limited by the value of the block reward
This is a good point too, but slightly incomplete: it's the total of resource consumption that depends on the value of the block reward. So if the energy consumption goes down, competing miners would buy more hardware, which moves the pollution to a different location.
The electricity will be reduced by the fact that Round 1 is not computing-intensive and most of the miners won't be "allowed" by the rules (if followed) to advance to the second round.
What's stopping the remaining miners from doing a "51% attack", trying to beat the select few by creating their own new Round 1 followed by their own Round 2?