Why in the world would it be anyone other than Fitzpatrick? While playing in Tampa, Fitzpatrick guided Josh Allen on what to expect playing QB for the Bills, living in the local community and what he could expect from the media, fans and franchise. Allen is on record saying how much Fitz helped him break in to the league. He's respected by teammates and coaches, very well liked, very intelligent and has years of experience to offer Tua.
You can't have Rosen as the back up because he has nothing except competition to offer the rookie. Either keep 3 or suck up the failed trade and move Rosen for what you can get.