Gentlemen... success at long last! Based on your feedback, and some very useful gouge from a personal friend and B-Body guru, I was able to isolate the problem down to the fuel system. We were able to rule out the fuel tank, fuel lines, and fuel pump as the problem, which led (as most of you already knew) to the carb. It came with the car, but I believe this is a cheap knock-off of the Carter BBD... less than $60 on eBay. Anyway, when I cracked open the carb, we discovered that the middle gasket (between the upper valve assembly and the lower float/bowl assembly) was misaligned and pinched off in one place. As a result, it was likely impeding fuel flow through the carb.
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Advanced Auto Parts didn't have a matching gasket, so we fabricated the missing section out of gasket material, reinstalled, and closed the carb. We also replaced the in-line fuel filter because it was old... however, didn't look very dirty or clogged. After those two mods, she fired right up. Success!
After a trial drive around the block, my only issue now appears to be a super-fast idle while driving... to the point where the car gains speed w/out my foot on the pedal when idling down the road. That, and the engine revs very high when I put it into Park; much higher than the fast-idle setting, for example. This usually remedies itself with a tap of the gas pedal, but still unusual. Perhaps a sticky throttle lever, or other issue with the brand-new transmission? Dunno... but I'm clearly on to my next adventure. would love any advice on the NEWEST issue of 73-won't-run-right, but I am hugely grateful for the help so far. I hope that this might be a useful troubleshooting for you in the future.