OK, tests in. There's a voltage drop all along the way, but grounds are good.

At Alt, no load 14.15 vdc
At Alt, loaded 14.03 vdc
Alt  to ground, same readings

At vehicle battery, across terminals, no load 13.73-75 vdc (.42 drop)
Vehicle battery, across terminals, loaded, 12.82-85 vdc (1.21 vdc drop)
Vehicle battery to ground, no significant difference

At aux battery across terminals, no load, 13.17 vdc (.58 drop from vehicle
battery, .98 from alt.)
Aux battery across terminals, loaded, 12.32-39 vdc (.5 drop from vehicle
battery, 1.71 from alt.)
Aux  battery to ground, no difference.

The worst problem here is what I suspected, a more than 1.5 volt drop
between alternator under load and aux battery under load. The more you load
it, the worse it gets. (I was using high beams, AC, and fridge.)

This is with the stock 23 year-old wiring and relays, but upgrades to
grounds. I doubt if any battery set-up would work right given these conditions.

Any idea what an acceptable voltage drop would be using new 6 AWG wire and a
new OEM-type relay? It seems like ideally, you could get 13.8vdc at the aux
battery under load--but how likely is that to happen?