Yeah, but the problem is that we actually have to construct and execute an infinite sequence of decisions when we say that we're doing something some number of times every round for Aleph(0) rounds. I might be completely misunderstanding it, but I think it's the same reason why you can't go from NI of something to Aleph(0) just by saying so. Remove the decision-making, though, and it's no longer arbitrary whether the cycle continues at a given iteration, and you can therefore actually take limits.
Can we figure out a way to automate the production of clones in a way that still fundamentally ties it to a current statistic? If I read it correctly, traps are fixed at Aleph(0) unless you can automate trap production.
AFAIK, the reason why linear decision making can never reach an Aleph is that repeating a process a non-infinite times per iteration for a non-infinite amount of time can at most give uncountable, arbitrarily large values (given the delay = 0), as opposed to infinites. Actions are limited in that you must perform them one after the other.
The reason you can't go from NI to Aleph (0) on, say, the Imp of Cania is that:
If the imp of Cania went to a timeless plane, did it's trick for ever, and came back, it would only have performed the trick an uncountable number of times. You can't reach Aleph (0) by waiting through time, as you have always spent a countable number of turns there.
However, my Pun-Pun gets around this by having a
known amount of time, namely Aleph (0). Assuming we perform each spawning loop at least once per round,
which we can, we will thus have an iteration number equal to or greater than the number of rounds.
(Input) ^ 2 ^ (Iteration Number)
About your other points:
Tying clone production to a statistic kills the process. By tying clone production to each clone (because remember, when we split it doesn't keep magic items), 2 is to the power of the round variable.
By tying it to a statistic, it would stay at (Input) + (Clones per use) * (Rounds). This is not nearly high enough.
Your traps are not Aleph (0). They are only NI; you are dividing by zero, which doesn't reach true infinities.