The crew certainly hasn't fully considered the implications of returning home at this point. Akon touched on it, humanity is something of an impostor as far as "not-stupid" space-faring species go. Whatever the outcome, the Lord Pilot has proven that humanity is capable of fragmenting and going to war over this issue. If the Impossible Possible World returns to human space then people will have both the motive to fight each other, and now the means to destroy themselves now that the Alderson cat is out of the bag.
Moreover it's quite possible that the "negotiations" were performed under a false premise. it seems likely that the Superhappies are aware of the capability of the Alderson drive, but they very well may not be aware of humanity's ignorance. The records sent to the Babyeaters were censored, particularly of technical data, so the coupling constant error might not have been there. Moreover Lady 3rd does seem remarkably sure that human decision-makers will make consistent decisions. This could be a result of assuming humans have dealt with the Alderson drive filter like the Babyeaters and Superhappies who are then both much less diverse than humans.
All that boils down to the idea that the Superhappies may be assuming that the modification of humanity will be a cooperative venture when in fact it is likely to be a species destroying war.
I guess the real question is does humanity thus constitute a "species in circumstances that do not permit its repair"?
It is possible that, like they Babyeater's attempt to convince the crew to eat their own babies, the Superhappy's arguments are also rationalizations when their most fundamental purpose is really eliminating their own pain. Thus they might be willing to trade away eliminating all human pain if modifying their own empathic faculty turns out to be the less painful-to-them alternative.
As to what the Confessor is going to do? I'm not sure. He could stun whomever is in control of the communications (Lady Sensory?) and transmit the relevant information to the Superhappies. He may believe the upside result to be better terms and the downside result to be the Superhappies enacting their compromise by force. He could feel that downside to be only slightly worse than voluntary implementation and significantly better than sparking of a potentially human destroying war.
Of course they may want to employ the slitting their own throats option in either case given the Alderson secret and humanity's posited issues.
Mind you to me there seem to be so many risks that I'd have to assume some special insight due to his commonality with Lady 3rd in order to be confident of making such a gamble on his own. It seems the risk adverse action would be to go back to Huygens and detonate the star the moment the crew arrive. This would kill every colonist, but would save the Babyeater's babies and prevent humans from learning how to destroy themselves (for the moment at least).