Solomonoff induction can be computed in the limit.
During round i, simulate your chosen UTM on each valid input string (note: assuming that the valid input strings are prefix free, which iirc is the standard for solomonoff induction) of length at most i, until you have simulated it for i steps total, or until it halts (whichever comes first).
When doing so, for any string, the proportion of the inputs (with respect to the coin flip measure thing) to the UTM that eventually halt with whatever particular output, which will have been found to halt , will approach "all of them".
Now, you can't quite say "run as long as you need to in order to get answer within this epsilon of correct answer", because you don't have a way of determining whether something hasn't halted yet but will, or if it never will, but, it is still computable in the limit. If you use absurdly (possibly quite absurdly) large but finite amounts of computational resources, it should give you a good enough approximation.
Humans make mental errors often enough. I don't see why one would think that, because solomonoff induction is only approximable, that that suggests human intelligence is uncomputable. Why not suppose that humans just have a very close approximation to the uncomputable thing, rather than the noncomputable thing itself?
Why believe that human intelligence is computable? Well, for me it is more of a "choosing not to believe that it is uncomputable". If I believed it uncomputable, I might hang too much of my philosophy/worldview on that assumption, and then if I turned out to be incorrect on that, too much might come crashing down.
Edit: note: I mean "not believing", not "disbelieving". Not(believe(p)) rather than believe(not(p)) .