Here's a thought: if you want relationships with the other couple then keeping it about sex will keep it, well, mostly just about sex. That's OK, of course, especially in the swinger arena. But if you want to be emotionally close then a swinger approach may not be what you're after.
A guys' night is a good idea, especially when endorsed by RP and HMA. Another thought is some time with the four of you together non-sexually. Day at the park with dinner afterward at a nice restaurant? A half-day road trip? I don't know what you all like to do, but maybe just being around each other casually for awhile will ease the nervousness. Or it may trigger something that tells you this couple is not what you hoped.
You describe your wife's emotions as ranging from boundless enthusiasm to abject fear. This might indicate that she doesn't know how to feel because she doesn't know the people well enough -- without understanding them and where they're coming from she's running wild between hope and despair.
Maybe besides being a helper you need to put on a calm-gentle-wise hat. Smooth the troubled waters...point out to your darling wife that as knowledge replaces speculation unfounded hopes and wild fears will fade, and that knowing people simply takes time. The other couple will also be feeling some of this craziness, and perhaps that's also topic for discussion with B, since she seems to be the dominant personality in the other couple. Or with H as well.
I dunno. You've described the situation in good detail but it's always hard for outsiders to know for sure what personalities are like and how things really are. You're the one who does know that, so take what I've written with healthy skepticism. Good luck!