The OP appears to be proposing something that will result in only 0.1% of the miners using their equipment in the second round of mining, and the remaining 99.9% of miners will turn off their equipment during the second round.

The above is not possible due to pool mining. As an example:
If there were 10,000 pools participating in the 1st round, only 10 would make it to the second round. Once the second round starts, the miners who were mining for the 9,990 pools that are not participating in the second round would switch to one of the 10 remaining pools.

There are currently 4 major mining pools (with the likelihood of there being more that are not public). Most likely, they would all be able to participate in the second round of mining, however in the event that one pool is unable to participate in the second round, the miners mining for that pool will switch to one of the remaining pools. If a "solo miner" would be able to make it to the second round, it would make financial sense for them to "sell" the ability for others to "mine in their name" and if no pools are able to participate in the second round, all of the pool miners would "buy" the ability to mine in one of the solo miners who are participating.

tl;dr - total electric consumption will not be reduced by implementing the OP's proposal.