I have few thoughts and questions.
1. This proposal reminds of how some DAG-based cryptocurrency works. When creating a TX on those cryptocurrnecy, you're required to verify few TX chosen by deterministic and verifiable random function.
2. Since the TX need to include list of cosigner, wouldn't it bloat the RAM and storage drive?
3. An attack seems possible in which the attacker creates transactions but refuses to cosign their assigned inputs. I think this was already suggested, but your reply was not clear to me.
When a cosigner is nonresponsive, the sender must replace their address. They must redact the first or previous transaction before publishing a new one to avoid having more than one version of a transaction in the mempool at a time.
Considering majority people don't bother run their own Bitcoin node or have server that online 24/7, it makes me wonder how many times the sender must repeat such process.