Of course, if our universe is undecidable it must be the case that computable processes can be executed within it, and it might be the case that all of the processes that are ever executed within it are computable... but it might be that some of the processes that are executed are not computable... because the machine may.. or may not?

I think there's an equivocation of "computable" going on here. Mathematicians talk about a lot of things like "uncomputable sequences" but that is usually making a statement about the sequence, not necessarily any individual member. The Busy Beaver sequence is uncomputable. You can, however, quite trivially compute BB(2), even in your head if you're a bit careful. You can set up individual elements of an uncomputable sequence in our universe, and you may be unable to state in advance what the system would do with anything less than simply letting it run and see what happens due to the complexity of the system, but being a member of an uncomputable sequence doesn't mean that you can't in fact set those things up and watch them run. The Universe doesn't throw an "UncomputableCircumstance" exception or anything. It just keeps advancing to the next state. Your inability to make certain statements about that next state or some future state is not its problem.