To shooter, kagliostro, jjailli, sluckey and others who may respond:
Many thanks. I had already made some voltage in/voltage out measurements using a crappy Chinese auto-former and equally crappy Chinese VOM. My results seemed so bizarre that I had to stop and question my entire methodology, and thus I posted my original query. I can already see, based on your detailed, thoughtful (and timely!) responses, that these OPT's won't be very useful in an amp that uses EL84's, 6V6's, or any other commonly-used output tubes.
I'm so worried about giving newbies ideas which might lead to trauma or death that I'm going to refrain from giving any specific information (schematics, voltage readings, etc.), and end this topic by stating it as a general rule that the SS jukebox transformers in question should be left alone, because you can easily buy a suitable new or used OPT for your tube-amp project, which has its specs clearly labeled, for less than the price of a good DMM, Variac or emergency-room visit... "Move along folks; nothing to see here."
But: I have recently started to figure out that the output tubes we guitar players know and love (6V6's, EL34's, KT88's etc.) represent just a tiny fraction of the gazillion different vacuum-tube devices that exist, and that an OPT that would be totally inappropriate for these tubes just might end up being useful to experimenters who know how to decipher a tube data sheet. I really am a serious Dumpster-diver who hates to see good stuff get crammed into landfills, and if I can find an inexpensive, readily-available vacuum tube that could be used with these hefty OPT's, I will post some (hopefully) thoughtful commentary.