lengthiness is not expected to be the only obstacle to finding a proof

True; stick a ceteris paribus in there somewhere.

You are trying to reason about reality from the point of view of a hypothetical entity that has infinite resources.

Not so; I am reasoning about reality in terms of what it is theoretically possible we might conclude with finite resources. It is just that enumerating the collection of things it is theoretically possible we might conclude with finite resources requires infinite resources (and may not be possible even then). Fortunately I do not require an enumeration of this collection.

I am certainly not saying that feasible proofs cause things to be true. Our previous slow computer and our new fast computer cause exactly the same number of important things to be true: none at all. That is the formalist position, anyway.

So either things that are unfeasible to prove can nonetheless be true, or nothing is true. So why does feasibility matter again?

P(I will prove the negation of your theorem in fewer than m+1 minutes) = p

No, it is > p. P(I will prove 1=0 in fewer than m+1 minutes) = p + epsilon. P(I will prove 1+1=2 in fewer than m+1 minues) = nearly 1. This is because you don't know whether my proof was correct.