I think it's an interesting idea. I like your insight about validation through cosigning.

I have some questions. Forgive me if they have already been answered.

1. How do you prove that the cosigners were chosen randomly?
2. How do you ensure that cosigners are available for each transaction and transactions are available to be cosigned? It seems like there is a balance that must be maintained. For example, a typical transaction has one input and two outputs. This implies a shortage of inputs available to cosign.
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.