That sounds rather like you are describing a half bridge connected to a centre-tapped winding - where does the positive output come from?
If you replace a half bridge with a full bridge, you will double the output voltage.
(Trying to visualise the setup from the description, so I may be wrong).
Not being well versed on the proper terminology, I will attempt to describe it in detail.
A/C is fed into the front of the transformer. One leg goes directly into the transformer while the other goes through the 6V/12V switch then two wires into the transformer and green goes to chassis ground.
Three wires come out the back of the transformer. 2 wires feed the two selenium rectifiers and the third wire is the battery positive which goes through the auto reset circuit breaker, throught the amp meter and out to the (+) battery clamp. The battery (-) comes off the aluminum plate the selenium rectifiers are riveted to and goes out to the battery negative clamp.
The two chargers I am currently working on are both designed the same way and both rated at 10 amps. They both also output roughly max 2-3 amps regardless of what battery i connect them to. As they slowly charge the batteries, the voltage will also very slowly rise to about 13.8v.
I have already taken the 2 spade terminals from the selenium rectifiers and connected them to the bridge rectifier A/C terminals and the wire from the selenium rectifier aluminum plate to the bridge rectifier (-) terminal and it charges 10-11 amps while quickly climbing up to 14.8v according to my Fluke 88 DVOM.
My idea is as stated earlier. To keep the selenium available for a slow charge while adding the bridge for a initial quick charge via a switch to determine high or low charging rates.
Also I picked up a box of five Volt Amp meters with 100a shunt. They are quite accurate and capable of 4-48v and 0-100a. I couldn't resist as they were at a local Amateur Radio swap for $1 each.
These chargers still function even though they are probably 40-50 years old so I though of bringing them more up to speed without going overboard.
I guess I should add the bridge rectifiers I have are KBPC5010 rated at 50a 1000v. A little overkill but they only cost me $2 each new. They are extras from a pair of 13.8v 35a regulated powers supplies I rebuilt.