Re "What I think I might try is buying some 10w 10-ohm resistors and wiring things up to drop the 5-ohm resistance down to 3 ohms to get voltage around 14.5 volts."
I think one problem you have is that 40 or 50 years ago the AC RMS plug voltage was 110 Volts RMS AC.
Now days most plugs in most homes are 125 Volts RMS AC, and some are a few volts higher than that.
The charger you have is a simple transformer and full wave rectifier (center tap). There is no regulator, and therefore an increase in the AC RMS in causes a proportional increase in the DC output that this set up provides. Unfortunately the voltage that 12 wet cell batteries should be charged to has not increased over the last 40 or 50 years.
If you add some parallel resistors to the series resistor used for trickle charging, you still have the problem of the DC full wave voltage being too high because the AC line voltage in is now too high.
What you require is a bucking transformer or a variac to drop the incoming 125 RMS AC down to 110 RMS AC, or a bucking transformer to drop the output of the units transformer 16 Volt Peak (+ diode drop voltage) down to 14 Volts Peak (+ diode drop voltage).
If you put three silicon diodes in series, they would drop about 2 volts, but those would have to be diodes big enough to handle the forward current, and they would require heat sinks that were each electrically isolated.