Basically your friend is feeling guilty. You are both very close and now that the relationship dynamic has changed she doesn't know what to do. She doesn't want you to think she's abandoned you, so she wants to involve you in the things that she and New Boyfriend are doing. And she'd love to set you up with one of his friends so you could all go on happy foursomes together and live happily ever after.
In fact you could just solve this problem instantly by marrying New Boyfriend's brother or best friend.
All joking aside though, it sounds like she's a really good friend and really cares about you. Equally you sound like you have your head screwed on and don't mind at all that she has a boyfriend.
So just explain that to her. Be firm and don't use any excuses. Telling her that you felt that he didn't want you coming along was like pressing a panic button - she went into overdrive trying to compensate.
You have to tell her that you really appreciate her involving you in everything, but that there's no need. Tell her that you don't feel left out and that you know you can join them if you want to.
Arrange to do something regularly, just the two of you. Go for a drink, the pictures, whatever. That way you'll show her that you know that New Boyfriends don't replace Old Friends.