threshold-- yes.

I think any non-tokenized L2 will be fee-based, so the fees will incentivize participation. But only progressive miners will run such software in the beginning, and fees will be need to be balanced such that they are as low as possible for the users while still incentivizing participation among miners. If the fees start low, then few miners will care; if fees start high, then users won't care. So I imagine dynamic fees controlled by the market will be appropriate. And with good network effects, even low fees can be profitable if there is enough volume. Right now, Lightning is practically unprofitable, right? I don't know anyone running a node who makes any real money from it; it's always a passion project. But a miner could subsidize their costs and diversify (and possibly stabilize) their income by participating in L2.

I think you are probably right about the clock time issue; I was imagining looking at the transactions in the block to compare to ones that were in the mempool at each of the following blocks, but that is misguided because in the adversarial condition, the cheater would just use the old mempool to create a block. Perhaps instead of sending the block to other miners, the block could be sent to all L2Ss, at the time of creation. Barring that, maybe we would have to use the current/recent block, and just deal with the conflict in a different way.