Sheesh; no excuse not to back up your BIP-39 mnemonic phrases using SLIP-39 (Shamir secret sharing):
Anyway, I decided I didn't want to migrate my wallet, so I'll look into this. Arbitrary key support is also interesting. Thanks for the tip!
Using the app, we actually produce the SLIP-39 recovery mnemonics from the underlying BIP-39 seed, and since we can recover the underlying seed, we can regenerate the BIP-39 mnemonics, and import that into a standard hardware wallet.