Ok, so how about this work around.

The current approach is to have a number of human intelligences continue to explore this problem until they enter a mental state C (for convinced they have the answer to FAI). The next stage is to implement it.

We have no other route to knowledge other than to use our internal sense of being convinced. I.e. no oracle to tell us if we are right or not.

So what if we formally define what this mental state C consists of and then construct a GAI which provably pursues only the objective of creating this state. The advantage being that we now have a means of judging our progress because we have a formally defined measurable criteria for success. (In fact this process is a valuable goal regardless of the use of AI but it now makes it possible to use AI techniques to solve it).