So followup...
I finally got it all pulled apart and discovered the source of the leak: one gasket on the main header was in cock-eyed... in fact, I'm amazed it never leaked before as it's clear this thing wasn't set properly when it was last assembled (I suspect it's been worked on before).
So I ordered a new gasket set online, as well as a new set of carriage bolts (all were rusty, one snapped while trying to take it apart). Cleaned the fins nicely by soaking the heat exchanger in a tub of diluted CLR and rinsing them with a gentle spray on the garden hose.
When I went to reassemble it, I was cleaning off the gasket seats and found a bunch of small cracks between some of the holes in the small manifold, that I patched up with some JB Weld.
I finished reassembling everything, with some Vaseline on the gaskets (I know, I know, but they'll probably still outlast the whole unit before we either need to replace the whole thing, or sell the house) and some high-temp copper anti-seize for the bolts, and fired it up...
SUCCESS! No leaks, and I swear it heats better now than it did before (under 24 hours to get an 80,000 liter pool from 69F to 82F).