I think you have it correct, but so we are super clear here is how it works for
you send 1 card from each element.
Vang sends 1 card from each element
glenn's sends 1 card from each element
TrOs have a list of 1 card from each element. (because there are 3 competitors in fire)
any card on at least 2 lists is banned for all Fire vs Fire matches.
these bans do not affect any off element duels (eg. they do not affect fire vs darkness matches)
these bans do not affect any in-element duels for any element other than fire