Exactly, you have to tack on quite a few "provisos" in order to argue it's impossible. There are in fact many ways to circumvent incompleteness upon which every theorem you've quoted depends. Goedel machines have actually been built [1], so their existence isn't just theoretical.
Edit: to see another way forward, consider alternate/finitistic arithmetics [3] which are neither stronger nor weaker than Peano arithmetic, but which do not exhibit incompleteness. Arguably, Goedel's theorems pass due to the inherent infinities of the successor axiom, but with an arithmetic like Andrew Boucher's system F (not to be confused with system F in programming language theory), no successor axiom exists, and so we cannot assume that the set of numbers is infinite, and we can enjoy full induction without difficulty. There is still a lot of surprising territory to explore in the foundations of mathematics.
>Exactly, you have to tack on quite a few "provisos" in order to argue it's impossible.
I wouldn't say it's strictly impossible. I would say the limit is environmental, rather than no limit existing. At a certain point, the available signals from the environment are as precise as they're going to get, the mind is as informed as it's going to get, and no further improvements are possible without a whole complicated raft of new experiences.
Kinda like how science often hits the point where we can't actually shift into a new Kuhnian paradigm by pure deduction, but actually have to do expensive, difficult experiments.
[1] http://people.idsia.ch/~juergen/agi2011bas.pdf
[2] http://people.idsia.ch/~juergen/selfreflection.pdf
Edit: to see another way forward, consider alternate/finitistic arithmetics [3] which are neither stronger nor weaker than Peano arithmetic, but which do not exhibit incompleteness. Arguably, Goedel's theorems pass due to the inherent infinities of the successor axiom, but with an arithmetic like Andrew Boucher's system F (not to be confused with system F in programming language theory), no successor axiom exists, and so we cannot assume that the set of numbers is infinite, and we can enjoy full induction without difficulty. There is still a lot of surprising territory to explore in the foundations of mathematics.
[3] https://golem.ph.utexas.edu/category/2011/10/weak_systems_of...