... the Print Template saves all kinds of information besides the size.
Hmmm...I just tried this experiment...
Now that I have all of my paper sizes back via the procedure I outlined above, I opened an image and created a Print Template for it. I then opened another image and accessed the Print Template and, as expected, the correct paper size came up.
Then I went back and deleted (renamed) the .UDG file that contained all the paper sizes for the iPF6400 printer driver. Then I went into LR and pulled up an image, loaded the template I had just created and... the custom paper size was not available.
So, I believe the Print Template does save the setting for the paper size. However, if the current printer driver does not contain the definition for that paper size, you are out of look. As Andrew stated, the driver is a different issue altogether.
My problem was that when installing LR and the printer driver from scratch on a new hard drive, the custom paper sizes I had created in the old printer driver on my old system were lost. After performing the experiment I just described, I don't believe those paper size definitions are saved in a Print Template. They are apparently REFERENCED as a setting in that template, but without the .UDG file, the definitions themselves are unavailable. Those are what I was lacking.
I see now that I invited some confusion when I originally posted...
...My old C drive has LR6 installed and the print module has a large amount of custom paper sizes I've defined...
I should have stated "printer driver" and not "print module".