If you don't need the bail, Tatonka offers a slightly higher one, 850 ml or what?
GSI offers lower ones without bail, rather a big cup than a pot. Tatonka too.
A hanging pot over wood fire works much better than a cup that you just put at the side, especially if you want to cook and not just boil water for a tea.
One can do without of course, but it's better to have a bail.
The bail attachment stands out though and it might not fit in every pouch that fits to a Tatonka or GSI mug.
All these mugs are common like your bottle. I guess they all fit well but I don't know that exactly. Because I own just the Toaks mug but no Nalgene bottle of that volume. But you surely can research the fit easily. Who sells the mug usually offers the plastic bottle with it. And you can use the search function of the forum to find some owners of the mugs, if not directly Google will give you an answer. Does every American own a Nalgene bottle or just every third?
Every usual outdoor sports shop that I have seen sold the Nalgene plastic bottles and some of the mugs that I mentioned above. It seems to fit well, everything else would be a big surprise.
I think these mugs are made to fit these bottles. And the red 100g Primus power gas cartridge fits also relatively well, by the way.