As others have said, you are either going to have to make those boxes work, or build something custom... Those are almost certainly proprietary, so you will be mostly on your own for building...
A plastic box is nice in that you don't need to worry as much about insulating the outside of the packs, but a sheet metal box would be easier to make... A reasonably decent sheet metal shop should be able to turn out a custom box without a lot of trouble....
Ah rating is not a highly useful number for telling what size a battery is... Better is to have the 'Group Size' if not the dimensions... This is the first thing I found w/ Duck-Duck -
https://www.batterystuff.com/kb/tools/bci-battery-group-sizes.html Sounds like you might have size 'U-1' batteries - which is not unusual for a portable type chair - they are small and underpowered, but light as lead bricks go... Unfortunately I don't know if we have any 'recipes' for battery sizes that will work for them. It may also be a challenge to come up with a pack that can supply the required current in such a small size.
It may be worth looking at the chair design to see if it would be possible to fit a larger box or set of boxes...
ex-Gooserider