Hmm. At least it's still fine to define limits of the complexity for infinite strings. That should be unique, e.g.:

lim n->\infty K(X|n)/n

Possible solutions that come tom mind:

1) UTMs are actually too powerful, and we should use a finitary abstraction to have a more sensible measure of complexity for finite strings.

2) We might need to define a kind of "relativity of complexity". This is my preferred approach and something I've thought about to some degree. That is, that we want a way of describing the complexity of something relative to our computational resources.