I don’t know how you can recover the BAT, but you can transfer your BAT into your Uphold Wallet for safe keeping.
The gist is that Brave credits BAT to your Uphold Brave Wallet. You can use Uphold to transfer the BAT into your Uphold BAT Wallet, which is distinct from the Uphold Brave Wallet, and which Brave cannot touch. This is commission-free as it is still within Uphold, but now your funds are safe from Brave.
Instruction linked below.