When I think "not computable" I think of things which aren't implementable as computations. For the definition "implementable as a computation of finite length" versus as a program of finite length, pi seems to become incomputable... so that use of incomputable is weird to me.

I do believe that we agree. Creating a different solution to the liar paradox requires us to abandon formalism... but as far as I am aware the whole point of formalism is to give us good criteria for when our answers are satisfying, so I don't really see how abandoning it helps.