If I were in your situation with your background, I would go for Montgomery Ann, for sure. Family names are important to me, too. I agree that the other versions are a bit watered down to honour your grandmother. She will own it and make it her own and no one will think it is the slightest bit odd after she is a few weeks old. It's classic, strong, different yet very useable. We're like minded, though, I suspect. I named my daughter Benedikte (she is half German with a very German last name) after my grandfather, Benedict and a long line of German Aunts names Benita. I don't regret it, I love it in fact. We have to give a 5 second repeat/explanation when someone meets her and we always add, "you can call her Bea". Works just fine, no burden and almost everyone thinks it is interesting if they don't outright love it.
Love it! If it wern't a family name I would be hesitant but it being a family name I want to beg you to use it! Montgomery Ann is pretty, but what about Montgomery Olive, nn Molly/Mollie? I like the unexpectedness of Olive in the middle, I'm not a fan of Ann in the middle as it seems rather over used to me, but maybe with Montgomery being more out there that's not a bad thing. Or is Ann also a family name? I also love the nn Maggie. Please, Please use Montgomery as her first name!!
Wait was it mentioned that you have a son named Jackson? ... Having another child named Montgomery (boy or girl) is slightly terrible, please look at a map if you don't know what I'm talking about. You'd really have to name your third child Chattanooga instead of Charles, okay well Savannah or Tallahassee could work I suppose. Honestly, images of Confederate flags flash before my eyes so unless you have deep deep ties to the South, I'd move on to find more meaningful, less geographical ways to honor grandma.
I'm not usually a fan of unisex names/surnames for girls but I love when people use family names. Montgomery Ann is very sweet. I also like Montgomery Olive nn Molly. Maggie, Molly, Monty, and Merry are all great nns.
If I were in your situation and it would make my grandmother happy, I would not hesitate to use it. I personally wouldn't mind having this name, especially if it meant a lot to my family.