In principle there's no clear distinction between a prefix which encodes an entire new language and a prefix which just sets up a function to take advantage of the regularities of the string.

Yes, and this is important to see. The split between content and context can be made anywhere, but the meaning of the content changes depending on where the split is made.

If you allow the prefix to change then you are considering string lengths in terms of the base language. This language can bias the result in relation to the problem domain that you are actually interested in.

As I said above:

For example if I want to compare the complexity of 3sat expressions, then I shouldn't be considering algorithms in domains that support multiplication.