I never got that reply from Jameco, asking them to provide a schematic from the manufacturer that would show how the internal static shield is connected.
Yeah, that was a long-shot. I wasn't expecting that you would get anything. How would they know? Why would they care?
IF it does have a shield, and it doesn't appear to have a separate wire for it, then they probably connected it to the transformer core. (Which is a good place, IMHO)
Further, without a load I measure 119V on the output, while the input is getting 121V.
My understanding is that all transformers have losses and for that reason the 1:1 transformers should not actually have actual 1:1 ratios. As I understand it I should be getting more than 121V on the output, without a load, so that I would get a 1:1 ratio once I plug in a load. Is that correct?
Since this transformer seems to be stepping down, slightly, should I just rewire it backwards?
If the transformer is really wound 1:1 then "rewiring it backwards" would yield exactly the same results.
What exactly is the issue with a 2V drop? What kind of drop are you seeing with a load? 1A? 5A? 10A?
Or should I just return this item and search for a better one?
What does "better" mean in this context? Remind us what is the problem here that you are trying to resolve?
If it were me, I would put a proper 3-wire supply mains cord on it. I would connect the green-wire PE (protective-earth) to the transformer chassis.
If the transformer has a shield, then it will be connected to the core/frame and the input source PE.
Your internal photos show a transformer that appears to be reasonably good for a hobby-level bench isolation application.
My only beef with it would be the lack of PE on the input/source wiring. And that is trivial to remedy.