Unfortunately I don't have any advice about ways to move in the right direction, but I might have an idea of why R sees it the way she does.
First, though- you say R is monogamish. Has she ever been in a poly relationship before?
I ask because the impression I get is that she (consciously or not) expected you to act more like a monogamous partner around her. I would bet that so far in your relationship, especially with it being long distance, when you are around her she is the only one receiving visible romantic attention from you.
Since it seems you and she were not on the same page regarding meeting J in the first place, I would bet you also did not talk about things that might be difficult or uncomfortable for her, ways you planned to act (to her around J, or to J around her), or what her expectations of the meeting were. It seems likely to me, then, that she quite simply did not completely think through what the possibilities were when meeting your other partner with you, and the actual experience created a cognitive dissonance that she's working through. She may be trying to put the blame on you in order to avoid working through it; I don't know.
I guess it goes back to communication. You didn't communicate scheduling the meeting well enough, apparently, and she didn't take the time to communicate to you what she wanted from the meeting, nor did she communicate with you in a timely fashion when she was unhappy with it. So now her expectations have been communicated. Without arguing about her perception (because I agree that's pointless) it might be time to say, "This is the way I act in public when I am with someone I am dating. If you are not comfortable with it, we need to discuss ways to deal with that." and go from there.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack