Good experiment! Actually the wood I used was not as rotten. I tried the Minwax wood hardener on another similar thing and while it penetrates quite well, the solid content is less than 20% and after evaporation of the solvent, the resulting wood is still quite spongy. So I went ahead today with the thin CA because that is what I had at hand. I did a rough cut first with a generous skin of about 1/10" so that tearout did not affect the final surface.
Then I let the CA soak in; the spalted wood sucks it up immediately and you are right, when applying too much at a time it starts fuming or even white foaming. The CA reacts with the wood within seconds. But applying in several sessions with a few minutes apart made it work without fumes. Then I did a finish cut, leaving another 0.015" skin, wiped on one more layer of CA and repeated the finish cut at the target depth. Took a little longer than a normal bowl but I think the result is worth it. There are still a few small rough spots that I could not sand out but overall I am quite happy with the result. It is sanded up to 500 grit plus steel wool and finished with natural, unpigmented wood stain. Given the 98 degree temperature outside it dried up within an hour.
The curly figure is spectacular and it might even have looked better without the spalting.