That top photo looks like a connector. If you can find another I guess that is a male connector to go on there then you can do things. Anyway when I said switches I meant like the following
View attachment 39046
On the right is effectively what you have now, which is to say a battery and a load for it. Excuse the crudeness of that; I only had Fritzing here to play with.
On the left is what I would propose you consider and dodge the charge management issues (or at least have them remain the same as whatever they were at the start of all this -- battery charging is more than just apply a voltage for a while which is what I fear this controller is doing now). The switch is there to allow you to select between batteries with a simple slide switch, the capacitor is an optional extra and will allow the controller to still work for the fraction of a second between swapping over via the switch.
Depending upon what you want to do with even further batteries or finding male connectors then you might wish to go to a DPDT (double pole, double throw) but that is a trivial change.