To me this feels quite a lot more natural than the previous version. It's not clear whether the vulnerability to threats is a positive or negative feature.
Part of your stated original motivation for exploring this was that traditional bargaining solutions didn't deal with power. We could adapt your solution here to define a defection point: the scenario where the first agent has the negative utility function of the second agent, and vice-versa. Then we could investigate the Nash bargaining solution with respect to this defection point. Without more thought (and perhaps playing with some examples), it's not obvious to me if that's better or worse than your proposal here.
Though I planned to avoid posting anything more until well after baby, I found this refinement to MWBS yesterday, so I'm posting it while Miriam sleeps during a pause in contractions.
The mutual worth bargaining solution was built from the idea that the true value of a trade is having your utility function access the decision points of the other player. This gave the idea of utopia points: what happens when you are granted complete control over the other person's decisions. This gave a natural 1 to normalise your utility function. But the 0 point is chosen according to a default point. This is arbitrary, and breaks the symmetry between the top and bottom point of the normalisation.
We'd also want normalisations that function well when players have no idea what their opponents will be. This includes not knowing what their utility functions will be. Can we model what a 'generic' opposing utility function would be?
It's tricky, in general, to know what 'value' to put on an opponent's utility function. It's unclear what kind of utilities would you like to see them have? That's because game theory comes into play, with Nash equilibriums, multiple solution concepts, bargaining and threats: there is no universal default to the result of a game between two agents. There are two situations, however, that are respectively better and worse than all others: the situation where your opponent shares your exact utility function, and the situations where they have the negative of that (they're essentially your 'anti-agent').
If your opponent shares your utility function, then there is a clear ideal outcome: act as if you and the opponent were the same person, acting to maximise your joint utility. This is the utopia point for MWBS, which can be standardised to take value 1.
If your opponent has the negative of your utility, then the game is zero-sum: any gain to you is a loss to your opponent, and there is no possibility for mutually pleasing compromise. But zero-sum games also have a single canonical outcome! For zero-sum games, the concepts of Nash equilibrium, minimax, and maximin are all equivalent (and are generally mixed outcomes). The game has a single defined value: each player can guarantee they get as much utility as that value, and the other player can guarantee that they get no more.
It seems natural to normalise that point to -1 (0 would be equivalent, but -1 feels more appropriate). Given this normalisation for each utility, the two utilities can then be summed and joint maximised in the usual way.
This bargaining solution has a lot of attractive features - it's symmetric in minimal and maximal utilities, does not require a default point, reflects the relative power, and captures the spread of opponents utilities that could be encountered without needing to go into game theory. It is vulnerable to (implicit) threats, however! If I can (potentially) cause a lot of damage to you and your cause, then when you normalise your utility, you get penalised because of what your anti-agent could do if they controlled my decision nodes. So just by having the power do do bad stuff to you, I come out better than I would otherwise (and vice-versa, of course).
I feel it's worth exploring further (especially what happens with multiple agents) - but for me, after the baby.