The badassBox website says it works with E8000 firmware up to 4.7.0: https://www.badassebikes.com/en/a-210/
Have you considered the software-only option? I think they're superior because you're not fooling the motor, the motor knows exactly that it's doing. You're working with the motor, rather than against it, in other words. The software is giving you options that already existed within the motor, but were hidden from the user (which is why the correct speed is shown on the display).
The two software-only options are STunlocker and eMax. Both are potentially cheaper and more flexible than the badassBox. I have no connection to any of the above (and actually dislike the developer of STunlocker after he attacked a user of his product in another forum), but I prefer the flexibility of the software-only solutions, and they can do a lot more things. You can tune every level of assist separately for max speed (between 25 and 60 km/h), max torque, max assist percentage, and max wattage.
I just read up on the badassBox (I had heard about it but knew almost nothing about it). It appears to be only a derestricting device, whereas the software-only solutions are full tuning alternatives. So I guess it depends on what you want but I just wanted to make sure both options were on your radar.
To me the primary advantage of the badassBox is that it can be easily disconnected for bringing it into a bike shop, but if your motor is out of warranty then why does that matter? It does work with newer firmware though. You can fake the wheel size on newer firmware as a way of derestricting with eMax or STunlocker, but for full functionality, you would need to downgrade to firmware 4.3.2.
tldr; firmware 4.7.0, apparently.