As a final touch, I used this foaming A/C coil spray to try to push everything out of the condenser, ATF cooler, & oil cooler fins. The rinse water didn't come out brown like I hoped, but it did shoot through to the radiator better than I expected, so I guess there's nothing in there to block the air.
I can't say that this stuff worked any better than Gunk Foamy Engine Brite would have, so that's probably what I'll use if I ever have to do this again.
At some later point, I realized the fan clutch had stopped locking, so I replaced it with an
ACDelco 15-4674 Fan Clutch from Amazon.