I just looked up something on the Yugioh wiki regarding Paradox, and his character. and I have come to a really weird conclusion judging by his "return" In the "Duelist's United" Movie Trilogy:

What if the Paradox we knew in BBT and YGO 5ds isn't the same Paradox in DU (Duelists United)?!

What if Paradox also had a counterpart like Crow and Jack (and maybe Yusei) in ygo arc v, and he too had a far different character personality, unlike the BBT and 5ds version of himself.

Who knows Maybe we could even have three paradoxes?! All with different personalities and outcomes for their "hopeful future"?

That would explain why Z-one (who I thought is Zero, but maybe he's a new character/villain for the last part in the DU trilogy) thought of the Paradox from bbt and 5ds to be like family. While the other Paradox(es) haven't got a clue, while having families of their own.

Kinda like what the Paradox of DU is!!!

He never mentioned Z-one and Z-one probs won't be mentioned in any of the other movies of the DU trilogy. Also he has a daughter, named Lyra and his malefic monsters (plus the same abilities and d-wheel), he mentioned he lost his wife in the second movie, but we don't know if it is because of a cardgame she, or someone else played (probably Zero), or something far more serious.

Also I was under the impression Zero was Z-one's dub name, but thanks to ygo wikia I was sadly mistaken. Forgive me! I believe I too have seen the error of my ways and unlike the Paradox from bbt and 5ds...hopefully so will Paradox's DU/Arc v counterpart...

Unfortunately I will miss both Paradoxes being the maddest villians of ygo history. RIP BBT and 5ds Paradox(S) and maybe also DU/Arc v. T-T Yu will be missed terribly.