Redefining "utility" like this doesn't help us with the actual problem at hand: what do we do if Omega offers to double the f(x) which we're actually maximizing?

It wasn't intended to help with the the problem specified in terms of f(x). For the reasons set out in the thread beginning here, I don't find the problem specified in terms of f(x) very interesting.

In your restatement of the problem, the only thing we assume about Omega's offer is that it would change the universe in a desirable way

You're assuming the output of V(x) is ordinal. It could be cardinal.

all this means is that Omega is offering us the wrong thing

I'm afraid I don't understand what you mean here. "Wrong" relative to what?

which we don't really value.

Eh? Valutilons were defined to be something we value (ETA: each of us individually, rather than collectively).