Obviously the rifle pictured below has all the general characteristics of a #16, but I am asking the question because the barrel is round full length and all 16's I have seen had barrels with the octagon to the end of the forearm and then round to the muzzle. It is an 1882 model and the caliber is either a 38-50 or 38-55.
Any thoughts?

Yes, it is a model 16. The pistol grip butt stock with the swiss buttplate, rack and pinion sight and forend make it so. Most #16's had the 9" octagon barrel but full round barrels were an option and having it would not make it wrong.

Check the chamber to determine if it is for the everlasting or standard case. Most auction houses don't know the difference and most can't get Maynard calibers correct because the barrels aren't marked as to caliber.

Does it seem heavy enough to be called a Dover barrel?

What is meant by Dover Barrel?

I received my new Maynard today, everything I could hope for. Very nice in excellent condition with a mint bore. It is a 38 and I will cast the chamber to determine the exact chamber dimensions. The twist is 18, as it is stamped under the barrel near the pivot lug. The function of the action is very good and the lockup solid. BTW the lever is plated the same as the buttplate. Its a grey color so not sure if its nickel or silver. (Probably Nickel)
The sights are a Maynard mid range rack and pinion tang sight and the front is a #7 Lyman windage. The front is the first I have seen of these and they are really nice.
As I said at the start I am very pleased. Should be a great shooter.

As I said previously, I have cast and slugged the bore. The rifle is chambered for the 38-55 case. The chamber including the rim gap is 2.110" and the neck diameter is .416" diameter. That is larger then the standard 38-55 (.394) but matches the 38-50 Maynard. I suspect the rifle was 38-50 at time of build but later re-chambered to the 55 case, most likely because of availability of cases once Maynard closed their doors.
The bore is .374" and the groove is .380. Leads me to believe it was designed to shoot a .375 paper patch bullet, however just my opinion.
I also was able to buy a new unused box of Winchester brand 38-55 ammo for $40 so I am set for cases as well.

I will make my own later this month. I intend to make both a PP mold and a grooved bullet mold. I make mine point pour. I am looking at a ~1.150" long design and will first design in cad so I can estimate weight and fine tune design. I am think weight in the 260 to 280 grain range.

It sounds as if it the chamber may be for the everlasting cartridge. What does it measure at the base of the cartridge?. Check it out before attempting to fire it or you may get a split case and a face full of hot gas.