Draft strategy for a 14 team, 19 players/team league

I’m struggling with this. I’m in a work league where the commissioner expanded the rosters to 19 players, and there are 14 teams in this league (that’s 266 players off the board just in the draft). Going late round QB seems to be a non-starter, as in all the mocks, most starting QBs are gone by the 12th round. Ruhning into the same with Kicker and Defense, being gone by round 16-ish. Would I be foolish to play normal-ish strategy, taking QB, D and K in the 12-15th rounds, and then going with the prayer-position players? Also, its a standard scoring, redraft league