> In case IL is 0 or ≥n, the master key is invalid.
Also I can't see how I would use this to seed a hardware wallet that requires a BIP39 seed as mentioned in your abstract.
For both of those reasons, you may want to just invent/formalize a scheme that takes Cards -> Entropy.
From that Entropy one can generate BIP39, and non-BIP39 fans can just continue, generate and store their root xprv.
Prior art: Note that Ian Coleman's BIP39 site already supports Cards (and Dice), see the logic here: https://github.com/iancoleman/bip39/blob/master/src/js/entropy.js
Note it detected "full deck". It also calculates the Total Bits of Entropy and can handle card replacement and multiple decks.
PS, you're a bit out on your entropy calculation, log2(52!) ~= 225.58 bits, not 219.