Was going to recommended Green Mountain but the only 32-40 barrel they list is a #2 octagon which is a little big for the 336. I have been having good luck with McGowen barrels, I buy blanks and machine what ever pattern I want. I use Green mountain if they have one with the right bore and twist ( best price). I don't use to many of their large bore barrel because they are eight groove and a lot of the barrels I do need six groove to replace originals. I also get quite a few Douglas barrels in, mostly from the same customer. The three barrels mentioned will shoot better than most people can hold and are among the least expensive.
The 1 in 16" twist is what an original would have. Groove diameter can run from .320" to .323" depending on who you talk to. It should be .312" bore with .320" groove.
I make my living at repairing or replacing barrels on old guns.