If N considers the program's length regardless of compressability, then you should be able to feed the "fake" halting oracle longer and longer programs that you already know will halt (like "print 1" "print 11" "print 111"). Since it actually gives reliable output after N, you can do something like a binary search (modified for infinite lists) to find its limit.
a binary search (modified for infinite lists)
By the way, one way of doing this is:
I don't think there's an optimal search algorithm for an infinite list of unknown distribution. Anyone know better?
Here's something I've been wondering about, in the context of Solomonoff induction and uncomputable sequences.
I have a device that is either a halting oracle, or an ordinary Turing machine which gives the correct answer to the halting problem for all programs smaller than some finite length N but always outputs "does not halt" when asked to evaluate programs larger than N. If you don't know what N is and you don't have infinite time, is there a way to tell the difference between the actual halting oracle (which gives correct answers for all possible programs) and a "fake" halting oracle which starts giving wrong answers for some N that just happens to be larger than any program that you've tested so far?
The Kolmogorov complexity of an uncomputable sequence is infinite, so Solomonoff induction assigns it a probability of zero, but there's always a computable number with less than epsilon error, so would this ever actually matter?