This appears to have scalability and security problems. From a scalability perspective unless mining is highly centralized you must communicate with many parties or process many signatures. From a security perspective a miner signing saying they'll mine a transaction doesn't actually prove that they're even trying to do so or force them to continue trying (e.g. if a higher fee comes along).
In each case, you must communicate with up to 2016 parties via a datagram, independent of the network size or transaction volume. Datagrams are small and cheap. You could blow out 2016 2kb datagrams at the same resource cost as blowing out a 4-megabyte jpeg to facebook.
Whenever there are far more than 2016 miners, you're still likely to get a statistically meaningful representative sample of the active miners out there. More resolution offers little practical benefit (n/2016 is already accurate to 3 decimal places, what would somebody do with more?)
Indeed, one might need to process up to 2016 signatures to have full confidence in the results. But if you're a retail POS terminal with a single user and an idle CPU 99% of the time, this shouldn't be a big problem.
This has the property that the proof of confirmation is actually also proof of really trying...
Just so I understand, how does p2pool collectively commit to anything? Include the commitment in a sharechain block?
What about traditional centralized mining pools? I agree that having proof of trying is a desirable benefit.
Unrelated, a calling card scheme might allow the miners to detect Finney attacks and coordinate the rejection of the block containing it.
As an example, upon receiving a block that invalidates a confirmation, an IPC-participating miner could broadcast a message to the other (up to) 2016 miners saying "Hey! I don't like block X because it forces me to fail on a commitment, and I propose attacking it." If the majority of miners send that message, they could follow it up with another message: "It looks to me like a majority of the mining power doesn't like block X, so I am attacking/ignoring it."