Right, just went and measured the battery tray. The distance between them is 210mm (8 1/4"). So that's the hard limit on length, and width is 140mm (5 1/2"). The battery clamps wrap around the end of the battery, so the width is a hard limit. Height is immaterial really as there's bags of room above.
Close up of the battery tray below.
Having had a dig through my somewhat ancient and dog eared battery cross reference table I reckon 054/5 is probably the best bet at 187mm (7 1/4") by 127mm (5") and 220mm (8 3/4") tall. 056 appears to be a high output version of the same thing - identical dimensions but 5kg heavier...so we'll stick with the lighter duty one methinks.
I'd rather avoid smaller capacity stuff like lawn tractor batteries as the generator isn't the most powerful thing in the world and I'd like to not be stranded the first time I get stuck in traffic with the headlights on for five minutes.
I know you can get far smaller form factor AGM batteries these days as well, but they're bloody expensive and seem overkill for this situation.
I open the floor to folks who have more current experience with battery form factor than I do.
Long term I reckon the battery may get moved to the front in the interest of providing a bit more ballast (offside of course to balance out the fuel tank) which would make this somewhat academic - though that's probably months or years down the line.
Edit: bit further digging has shown the U-1R (aka 895) is looking to be a good contender at 194 by 126 by 183mm. Interestingly being a "garden appliance battery" it seems to be cheaper as well despite spec wise appearing identical...