I opted to try the 34oz yeti yonder. Fits like a glove! Single handily operate without issues. Makes sure the flat side is square to the hip and it slides right in.
The nalgene that you have will work, it's exactly what i use. The bottle holder will eventually stretch a little. And i found if you use a twist motion going in and out it slides right thru.....
I use a big smart water bottle and it’s also tight, but a simple twist and it goes in… some times when it’s really wet, it will be harder to get it.. almost needs a grommet in the bottom to let air escape, but it’s not a huge deal
My bottle has the same fit as the couple Nalgene bottles I’ve used, i just prefer more volume and lighter