I'll give it another shot.
Opera House pointed to "circuit of 4-49 in that article." Here's the circuit:
Now imagine a "CR3" and "CR4" from the OTHER end of the transformer to A and B respectively. What you'll have is your charger with transformer and bridge rectifier, with the capacitors and resistors added.
With the capacitors and resistors in place the other two original rectifier diodes hang across the capacitors backwards. In normal circumstances they're always reverse biased and never conduct. But there's a bonus: In case of some trouble that tries to reverse-charge the capacitors these "unused" diodes will act as reverse-voltage clamps, limiting the reverse voltage across the capacitors to the forward voltage drop of the diodes, about 0.6V. This should be low enough to protect electrolytic capacitors from destruction by the reverse voltage.
So if you add the capacitors (and resistors) to your existing charger you turn it into a voltage doubling charger. Let's go a little farther: Put a switch in to disconnect (any two of) the three connections where you add the capacitors and resistors. Switch off, no doubling. Charger is as it was. Switch on, it's a doubler.
But why use a two-pole? Just disconnect the MIDDLE connection and leave the top and bottom ones connected. Switch on, doubler. Switch off, original charger with a series pair of capacitors across the output. (Plus the resistors: R1 and R2 act as "leakage balancing" and "discharge crowbaring" resistors. They keep the two capacitors splitting the voltage evenly during operation even if the leakage in the capacitors is unbalanced and gradually discharge the capacitors when the power is turned off. RL is just a load to keep the cap voltage from climbing unreasonably if there's little output load. With the capacitors the output voltage would tend to hang at the peak of the cycle rather than visit there momentarily as it does with just the rectifier.)
Resistor values: I'd pick this:
R1 and R2: About 12K. This pulls a thousandth of an amp. That should be large compared to the leakage of the caps and will discharge them eventually when the power is off, but will only eat about a fortieth of a watt when things are running. If you're going to leave the charger hooked to the batteries with the power off, leave 'em out and be sure your caps are rated 30 volts or more. Then they won't need balancing.
RL: Why bother? Leave it out.