To clarify my intents, this was a case of grabbing something before they are gone and then figuring out what I got. Now these look like they are nice isolation transformers so I went back and bought two more. The last two. Couldn't just leave them there.
I also picked up these two. Labels are good. CJLTT.
Using the separate primary windings works but the reasons it does not work well have been covered so I will not repeat.
If you have more than one of the same transformer then you can solve all of the problems. Wire two identical transformers back to back and ground one lead of each of the low voltage windings between them. Now you get full power and the grounded low voltage windings act as the electrostatic shield in addition to any shielding built into each transformer. The disadvantages are twice the weight and space, twice the power loss which is not a big deal, and twice the series impedance which may even be considered an advantage since it helps limit surge current.
I did this with a couple of 1000+ watt transformers and then wired the outputs to separate outlets so I actually have two outputs which are isolated from the power line and isolated from each other. Or I could convert either way between 120 and 240 with isolation if I had a need to do so.