That's certainly true, but Godel-type unprovability is separate from logical independence, and indeed much harder to make lists of.

My earlier point is not that we could know for sure that our struggles are due to being up against such a wall--just that our ability to suspect as much is relevant to how we allocate our time.

Oh, such as a list of statements unprovable under a specific Godel numbering? Definitely much more difficult - I never saw such a list in grad school, although I wouldn't rule out the existence of one.

> Godel-type unprovability is separate from logical independence

What do you mean by this? The Goedel sentence of a system is logically independent from the system by the standard meaning of "logical independence".