Just to be clear, you aren't really changing to a 6V system. You're replacing your existing 12V battery with a different 12V battery that is made up of two separate sections in series (each of which is nominally 6V).
This means, of course, that you need to have two 6V batteries. If you don't have space for two batteries, you can't use the 6V batteries, and need to find a 12V battery instead. From the pictures I can find, I assume you're constrained mainly by the width of the batteries but not so much by their length and could readily fit the two 6V batteries end-to-end across the tongue A frame.