I'm certain that the hood emblems said 3800, so it's a 1 ton chassis.
Not a good assumption. Never know what pieces have been swapped out in the last 50 years.
If the serial plate ID begins with 3E (or V3E for a V8) it's a 3/4 ton 3600. 3G is the 1 ton 3800. I don't think the frame stampings include these digits.
123" was the only wheelbase option for the 3600, and 135" was the only WB for the 3800. That is probably the easiest and most reliable way to tell between the two.
BTW, I'm nearly certain there was no factory Fleetside 1 Ton or any Fleetside box that is 9' during that run.