This is practically impossible to orchestrate on Bitcoin's network because some miners routinely broadcast empty blocks with no transactions in them except for the coinbase. On your own layer, you modify your protocol rules for all your nodes on L2 to reject empty blocks and the problem should go away. Miners will not waste their time mining blocks they know will be rejected.

But it would be much, much simpler for you to just use Lightning Network in a scenario like this.


You don't. What would happen is that the mempool on each node would just keep filling up until its maximum size and then transactions start to get dropped after that. Because new transactions can come at any time, shutting off miners isn't the solution you want.