Your situation is indeed a hard one, as it seems one of you can't be fully happy without a poly relationship and the other can't be fully happy with one. While mono/poly relationships exist, they are tricky and need to lot of work on both sides.
Saphena, you talk about maybe realising you are poly too. It's a possibility: my husband, when I came out, was pretty sure he was mono, but over the course of several months/years, he realised he was poly too, and had been rejecting it the whole time.
However, there is no way to be sure you're the same. You might very well be completely mono, and then it's important for you not to force it.
This being said, the relationship NonStick is interested in doesn't seem to require you to be poly. He wants a relationship with two women who share a bond, but that bond could be friendship. In that case, even being mono, that would be possible, since you wouldn't have other partners (male or female).
That doesn't mean you could be happy in a mono/poly relationship, though. It's something for the both of you to talk about and see how you feel, both of you, see how far either of you can go, see what compromises you could reach, etc. It might take a very long time before you find a satisfactory solution.
For you, Saphena, it might be helpful to list the reasons why you would have a problem with such a relationship. There is some level of conditioning, monogamy being the norm and all, so you'll have to find deeper reasons than the "that's just wrong!" and try and find more specific things that trigger your feelings (and which feelings these are). Then it will be easier to look at it and see what the options are.
For you, nonstick, it might be a good idea to think beyond your ideal scenario. First, how would you deal with two women who both love you and you both love but don't really have a strong connection? What about if either of these women has another partner as well? For instance, what if you do meet another woman and she is married too? And what about your wife, would she be "allowed" to have other people too? (Regardless of whether she wants to or not, it's good to ask yourself how you would feel about it).
And if your wife really wouldn't be happy in a V where you are the hinge (that would mean you are involved with two women who aren't involved together sexually and romantically), would you be happy with a traditional relationship with your wife and a platonic relationship with a woman your wife gets along with? Would she be happy with that?
I think it is worth exploring various scenarios and checking how both of you would feel about each one of them, that might help you know where you are standing.