I wouldn't assume A or B are the only choices.
"Now I think it's A. But if someone thinks it is B - then I'm curious. What exactly is happening with the autoformers that might be causing this?"
Why would you assume the autoformers are responsible for the differences you are hearing? The 2 amps are extremely different from each other, as are the speakers. Also, your tube amp has output transformers. They're not the same as autoformers, but they do perform a similar function. Either way, I don't think the differences you are hearing are caused by the autoformers. I understand why you don't want to try the set amp on the SF's, but you can try both amps with the Klipsch.
"In the same room, the tube-amp with Klipsch speakers seem to throw the sound all over the place while the McIntosh setup doesn't do that."
You need to try a couple of things. To start with, listen to the Klipsch/set setup. Play a song where the singer has a strong center image between the 2 speakers. When you listen, confirm that the vocals are where they should be. You could have made a mistake when connecting your speaker cables. It happens all the time. If the vocals are not between the 2 speakers, that's the problem. It will sound like the vocals are coming from one of the side walls. "Throwing sound all over the place", is a pretty good description of what that sounds like.
If your connections are OK and you are getting vocals between the speakers as they should be, listen to both setups again. This time you are listening for scale. Using that same test track, or something similar, are the sizes of the images bigger on the set? For example, does it sound like the singer is much larger on the tube amp? The difference won't be subtle. You will hear it immediately.