Since it has a flat battery, I think these should help
This should be an exact fit
This similar in size might be half an mm thicker
This is the highest capacity in flat form factor, It would fit but might take some convincing. I wouldn’t recommend anything higher.
Look on the site
For 500 you can buy 2-3 batteries and try to fit the largest capacity.
Also, don’t look for ultra-high capacity (>=4000 mah) those would be just 18650 in parallel and wouldn’t fit in the controller. 2000-2500 mah would be the most practical and you wouldn’t have to do a hack job.