I was thinking firmware is likely too. Why are there different firmwares?
The question for Axis is above, why or what changed between these firmware? Which one is newer? Is there an even more recent update than these you currently have? Maybe even a complete changelog would be nice to see.
The trouble is that users cannot update Zigbee device firmware using a file on Hubitat. In other words, if Axis did send you a file, it would be mostly worthless. At the moment, Axis (or someone) would have to send Hubitat the firmware and it would have to be added by staff, presumably Mike.
Also that whole updating idea might not work at all if the working one (1262-0013-03000800) is the older firmware, and the non-functional 109A ones were the newer firmware. Hard telling which is which, but my wild guess is that the 1262 is newer and that you need an update.