I think this is really lovely. People seem to have very different relationships with their children's partners so I think these threads will always end up a bit split.
My sister in law has been with my brother since they were teenagers and as I'm younger she has been in my life since I was 10. She would always be around our house. My mum and her are close. They definitely annoy each other sometimes but they love each other. My mum would not say she loves her like a daughter but perhaps like you'd love a niece.
Of course she'd always choose my brother if it came to it as that's her actual child but she would still care about my SiL and would be very unhappy if my brother treated her badly (and would call him out on it).
I have similar feelings about her - I don't love her like a sister exactly but I do love her and I'd miss her if they ever broke up and I'd want to see her happy.
Growing up I always kind of expected that that's how these relationships are and assumed that my relationship with a future MIL would be like that.
Hah!
I was genuinely astonished to find that after years of being "part of the family", my own in-laws apparently had no feelings for me whatsoever, would support my DH in treating me as badly as he wanted and even would try to set him up with other women while we were married.
I had always been polite with them, made an effort, always treated their son well (and put up with a lot more than a lot of wives would!) I even cared for him through very ill health.
It became apparent that it was not about me really. There was a very odd enmeshed relationship between my MiL and my DH, that she felt I had taken him away from her, that she wanted to be the one to "care" for him and my DH even described their family as "us against the world". Things weren't as bad when I was just a girlfriend but once we married and I was his family it's like they saw me as competition and always wanted to ensure they were his first priority.
I did not expect to become like a daughter to them but I did think they were my (extended) family and that they'd at least grow fond of me and care for me.
I would have done anything for a MiL like you who really made the effort. It sounds like you've got a great balance and honestly I would not worry too much about it being weird.
If the worst thing your sons gf has to worry about is that her MiL invites her to things she enjoys while being absolutely fine if she declines then she's got it pretty good. If she doesn't believe it I'd be happy to introduce her to the absolute insanity that I was part of.
Just be aware (sounds like you already are) and offer outs ("I know you may be working and so no worries at all if not. Just check your calendar and let me know if you fancy it..")
I think it's only be "too much" if you were upset at her declining or kept putting her on the spot and wanting to know why if she declined.
If she starts declining more often then pull back with the invites but if not then continue as you are. She's an adult too and she is more than capable of making excuses if she needs to, as we all do when we decline things.
One thing though... gently, your "who should I take?" idea is terrible. It would be very presumptuous of her to say "me" and would likely come across that she was actively not invited. Being honest while giving her a ready-made excuse and not forcing her to respond in real time face to face is plenty.