I checked the Trojan T-125 and it looks like it's slightly too big for the tray.
Out of curiosity, I went looking for a 6v that matched the width need. I found that the larger 6v batteries had more square-ish sizing than the long narrow rectangle I needed.
That got me wondering if there were any 6v that would fit. I found that a few BCI group L16 would meet the combined length and width need nicely but they are far too tall for the area under the step.
However, their height and bigger capacity makes them a very nice match for a different little project I have going on at home; can I safely run a koi pond exclusively on solar? Let's find out.