Welcome back - great to see you again.
What you're describing (feelings) aren't really unique to 'poly' - just maybe amplified a bit - or emphasized. And it's great that you noticed the exact discomfort in him. Because it's natural.
It's really just about the 'pairing' in a situation like this. There's a certain something in our brain that leads us to believe that if we arrive somewhere WITH someone that we will be interacting AS A PAIR. Of course, we all know, in a social situation that may or may not be the case all the time. So when inevitably the 'pair' gets separated and one has an interaction going and the other doesn't - bingo - brain doesn't know how to compute this. Seems to be breaking it's own rule ?
Some possible solutions ?................
Well, you already noted one. Don't inject yourself into what's happening between another pairing. Just move on and see what develops yourself.
Another is to just sit back, observe, and above all keep a big smile on your face ! If it's close enough quarters and he notices you he may well call you over to introduce you ! "Hey xxxx - this is my girlfriend Glow " ! And an interesting dynamic may come out there <wicked grin>.
But better yet, this is a great conversation for you and P to get into. Just a conversation about how a natural discomfort comes up when either of you end up odd-person-out. A good team would have a plan going in how to handle this in a better way than everyone for themselves. Maybe you guys can come up with such a plan ?
It's hard because every situation is unique. If an intense make-out session is in progress you obviously don't want to interrupt that. If it's just a conversation happening it may be fine to just wander in and introduce yourself.
If you two are attending parties and meeting others is a plan, and it's a party including people who are not poly aware or poly friendly it's not a pretty situation. Seems you almost have to go as singles ! Which I don't get the impression is part of your plan.
P is really putting himself in a delicate situation if he's hitting on other girls before acknowledging that he already has one GF (or more). He's liable to get his face slapped if the 'truth' comes out - especially if he's representing himself as 'available' when in fact that's only partially true !
Good luck Glow !