Thanks for the suggestion, but unfortunately that part is more money than I paid for the entire unit!
You're new at this, right? 
Seriously, there are some US sellers on eBay that have it, maybe have a look.
Eh, yes and no, have a few resuscitations under my belt so far: 2 out of 3 Fluke 8050A, 8840A, HP3466A, Keithley 197A and now this 177.
Tinkered some more. Turns out the DC modes actually were all working perfectly after I did a complete calibration, so odds were good for just the True RMS-DC converter being bad.
TP1 was 8V, but pin 6 on U103 (AD536AJH) was always -0.9V no matter the input or external adjustments. I tested all the components connected to it and they were fine. Found the data sheet on the AD536A series so was able to get all the pinouts. Pulled it out and it was for sure a goner. No chance getting this back to life with spare parts from the bin, though...
I was able to locate the similar AD536AKH from a reputable US seller for $20 delivered. Got it installed and ran once more through a complete calibration and all is well.
Cute 19,999 count relic for my "collection".