Sufficiently increasing the threshold N allows to prove that no other statements of the form [A=A1 => U=U1] will be proved before a decision is made (and so that the decision will be as expected). . . . This is the same guarantee that countable diagonal rule gives, albeit at the cost of having to know L.

Doesn't increasing N also change L? If N is part of the specification of the agent, then its value can affect the length of proofs about the agent. This indicates that there are probably agent designs for which we cannot just sufficiently increase N in order to make this diagonalization argument work.