This is dangerous terrain you are on. Not uncommon, but dangerous. I like what every one has said so far and agree. I would add also that meeting M is a really good idea.
Be friends first! See how that goes. Grow into this. It sounds like if you have a hope in hell of being V's boyfriend then you will have to spend time with all of them. Play this as two old friends getting together after re-discovering one another and move forward from that place. Rather than "tad da we want poly! I want to fuck your wife." As you said, he is not going to be receptive as is.
I wouldn't hold your breath for this to work personally. It might, but not without a huge amount of work and possible pain for all. Why not wait and see how it goes. Your girlfriend for starter needs informing of your intentions to get to know them better. Some boundaries need setting around that. She might not be open to you even getting to know V as a friend.
Might I suggest, from a lot of experience, "don't cheat!" Have a read here under a tag search of "cheating," and you will soon see why. The destruction that happens in the wake is greater than the sexual release. Remembering the pain and deceit will be all that's left, not the momentary bliss of touching her. Its NOT worth it, seriously. Everyone losses in cheating.
Anyone want to be friends on Facebook?
Send me your name via PM