I have only read a few replies, and sorry, I don't have time to read them all, but YANBU!!!!
I think the grandparent should definitely choose, IMHO, they have earned that priivlege. My Mum definitely always wanted to be Granny, although I had always hated that, as my GP were Gran and Nana. (Gran wouldn't answer if you ever dared kid her on by calling her Granny, and Nana suited being Nana.)
When my nephew was born, my Mum became Granny, and it was lovely, I even liked it. Now she is Granny to my 2 DS, and I love it. I would NEVER EVER have dreamt of insisting on Gran, or anything else. Sadly, my MIL is not with us, but she was Gran when she was alive, and I'd have asked her what she wanted. And RESPECTED that choice. We always called my Mum's Dad a funny name, which I can't say, in case anyone I know reads this, as it would immediately identify me, nobody ever called him Grandpa, or anything like that. If I mention him (he died 43 years ago) to people who don't know him, I have to explain why he was called that, and we laugh about it, cos it IS funny.)
I think Baba is a lovely way of honouring your family and heritage ( I knew a boy who called his Auntie, Bibby, right till she died, 'cos that's what he'd called her as a little boy, so there are lots of "funny" to others names around, which are perfectly fine for the families concerned.)
My boys call my Dad, Grandpa and sometimes my older one says, Papa. I personally don't like that, but if he wants to call him that, and Grandpa likes it cos sometimes he signs it on the nursery register, then it's fine with me.
I don't know what the answer is as you do seem to have a good relationship with your DIL, and it wouldn't be worth ruining. There have been some good suggestions e.g. Grandma Baba etc.
I just wanted to say I agree with you, YANBU. and congrats on a beautiful new GS to love and cherish. I'm sure you will be a fab Baba! (My boys are very very lucky to have such a fantastic Granny and Grandpa who absolutely dote on them.) Good luck.