This whole thing is probably an exercise in futility because it might be over a decade before someone does it again. But the best way to figure it out would be to work backwards. You're going to need at least 40 passing TDs from the QB. The number of offenses and/or QBs with that capability is pretty low. I'm guessing it could feasibly happen in Indy, Arizona, Carolina, Green Bay, NO, and Seattle. Both Brees and Palmer are getting old so they've got like a 2-3 year window (Brady will be too old the next time he has 16 games which is why NE was excluded, otherwise Gronk would be on the list). I realize Oakland and Jax both have young passers that hit the 30s last year, but I don't see 40+ happening - they both threw a ton of passes last year with minimal RB TDs.
Next, the guy needs to be able to both get deep AND be good in the red zone. Julio and OBJ would be good fits if their QBs threw enough TDs, but they don't. Antonio Brown is eliminated here (his historic TD/rec rate was way too low anyway). So, looking at the teams listed and this criteria, I've only got a few options:
Indy: Moncrief - speed and size, but I don't think he's actually good enough to warrant the targets needed.
Arizona: Floyd - best chance would be 2017 if he's brought back and Fitzgerald is gone, freeing up the targets he'd need. He's got the deep speed and the red zone size + ability. Palmer has never thrown 40, but he threw 35 on just 538 att last year. At that pace he'd need 615 att to hit 40 which is a realistic number in today's NFL.
Carolina: Benjamin - he's slow off the line but has a nice 5th gear so I guess it's possible, but I don't think that highly of him. Maybe Carolina will upgrade the position sometime in Newton's prime. Keep in mind Ted Ginn had 10 TDs last year on 97 targets and dropped 5-6 TDs (not hyperbole). If you put Julio on this team, he would be the odds on favorite to hit 20.
Green Bay: Jordy - the only problem is that Jordy probably has to do it this year or next since he's 31. He's good and Rodgers is great. Once had 15 TDs on 102 targets. But he's coming off injury and Rodgers spreads it around too much. The next guess would be Janis if he can put his game together. Has the size and speed, but is obviously a long shot.
NO: nobody - Brees spreads it around too much and nobody on this roster stands out in any way, much less has the ability to get deep AND be dominant in the red zone.
Seattle: Baldwin - he's not big or fast, but he did snag 14 TDs on 103 targets so I feel obligated to include him. I can't really see it happening for Baldwin, but this team will eventually be a pass first team and if you give Wilson 600 att, he's going to throw over 40 TDs. Maybe by the time that happens, he'll have a big, fast WR1. And an offensive line.