Thing is, if you went up to her at the first meeting Olea it could have been perceived as threatening or you imposing yourself.
If your ex is so bothered by his gf's ability to blend in with his friends, HE has to introduce HER, not pressure you into making the first move.
Sounds like he's totally bottled out here and is looking to be the man in the middle absolved of all social duties, hoping is past and his present make his life easier for him.
Without knowing precisely what was in his email to you, or her email to you it's hard to really know.
Suffice to say that anything more forward than, we hope you don't feel in any way uncomfortable being with us is OTT and bizarre.
I think in some way shape or form, she's acknowledged that she's been on the scene for over 6m and there's this seemingly lovely, popular woman who her boyf used to date, and she's the new one on the blockm she wants to know you're not unfinished business and her boyf seemingly has done sweet FA to allay her fears.
She's asked, he's dodged it, she's made it an issue, seeing it as a badge of honour. Not a real item until the ex is definitely and irrefutably apprised of the fact that 'he's moved on'
He's capitulated, and has said he'd contact you. Bet that there was more than one request, and in the end he did.
Now that he has, and you still haven't done what they wanted you to do, dutifully trot up and reassure her that you're so totally over 'her man' and we can all be best buddies etc etc, she's gone one step further, unable to contain herself and her probable insecurity.
Whether it's a scheme to get you to disengage (you said yourself it was putting you off going out with the group) or less complex than that, sommat's not right.
I'm wondering if she's making an attempt at being a Relationship Wendy.