Based on this quick and hardly thorough test, it would seem to suggest that the U2F is
not cross-compatible between different
brands of device, even with the same seed.

Thanks for doing that. It does raise the question of "Why are they different?" Obviously the same seed on a Trezor or on a Ledger will restore the same bitcoin or altcoin wallets, and U2F is an open source industry standard, so there is no reason that they shouldn't be cross-compatible. Are they using different versions of U2F maybe?
It does highlight the risky situation you leave yourself in if you use a hardware wallet as 2FA, though. If the manufacturer of the hardware wallet disappears or goes bankrupt, then you have no way of obtaining a replacement device and could potentially lose access to the protected accounts indefinitely. Based on this, I would not recommend using a hardware wallet as 2FA unless you have a second identical make and model in your possession as a back up.