It's working!
Would've been an interesting experiment to jump the secondaries, but no matter how I looked at it I couldn't figure out where I'd mount the second transformer. I let discretion be the better part of valor and picked up a used SPU (Socket Power Unit, or power chassis) on ebay for about $35 that claimed to have proper tested voltages.
Installed it in the radio, and bingo! Seems my diagnosis was right on the money.....I'm listening to the news on it right now