I intend to flip a coin 121 times, convert to BIP39 words and then enter them into my HW with a random 12th word until it accepts the mnemonic as valid (passing checksum). This way I'm not relying on the HW RNG.
There are a couple of problems with this idea.
The obvious one is that security-wise you want to generate at least 128 bits of entropy, so reducing it to something like 121 bits is not a good idea.
Additionally to do that, you need the hardware wallet to have had implemented a special procedure to first accept invalid and shorter mnemonic and brute force them to generate a valid one! Because that's what they have to do, to add the missing 11-bits or the missing word and check for validity, if it fails increment and repeat. They don't have such a feature as far as I know.