My final factual followup:

I flushed the trans cooler section repeatedly with acetone, and you would not believe the hideous gunk that came out. Some was hot-tank rubbish left over from the radiator shop, some was probably baked varnished old ATF. I blew it clean with shop air after the last acetone wash.

In retrospect, I'm incredibly glad I did not just slap this rad back in the car without cleaning it up first. I also noticed that the shop had given a quick spray with a not very well adhering black paint, and that they had gotten the paint down inside both main necks.

Yech. No way. I took another hour and cleaned off the overspray carefully with aircraft stripper, making sure not to leave residue inside. I then pressure flushed the unit through the coolant section, after dry masking the trans cooler ports.

A huge amount of ugly stuff came out, much of it big flakes of mineral crust with a green Prestone tinge. Happy to have that gone.

End result: rad is back in, car runs a steady 85C on water alone. I am doing a few drive-and-drain cycles to get out as much of the loose mineral stuff as I can before adding coolant; there is a bit of it visible still in the reservoir after every drive.

Note that this rad was dosed with citric acid at MB-recommended concentrations, and the citric just didn't get the heavy scale accumulation inside the tubes. Sometimes tougher measures are needed. And again, all this could have been avoided with a proper choice of coolant and the use of distilled water by the PO.