I've played Run and Gun for all but 5 games during 2 full seasons worth of games (started 2 seasons ago, 2 games into the season), and from what I've seen, place your third best shooter at SF, because SF still takes less shots. Something seems different, becausethe first third of this season, it seems my SG's taken more, but last season it feels as though my PG shot a lot more. I'll post some stats from a pure Run and Gun offense this season.
PG
Game One: 24 shots
Game Two: Innacurate- player got half SG, half PG for a game.
Game Three: 18 shots
Game Four: 21 shots
Game Five: 25 shots
Game Six: Innacurate- player positions were mixed up because one player played minutes at SG and PF, one player swapped PG to SG, a SG to PG, etc.
Game Seven: 36 shots
SG
Game One: 34 shots
Game Two: Innacurate- see PG note.
Game Three: 43 shots
Game Four: 22 shots
Game Five: 33 shots
Game Six: Innacurate- see PG note.
Game Seven: 34 shots
This statistic would show that SG takes more shots per game; around 34 a game as opposed to 26 a game for PG
Reviewing my statistics from last season though, my SG's took a total of 506 shots, but my PG's took a total of 489 shots.
Indeed, your shooter SHOULD take more shots each game from the Shooting Guard position; but I do find that the coach does not swap the PG as often; my calculations show that in the games above not labeled "innacurate", the starting PG plays almost 6 more minutes a game than the starting SG.
I'm going to go with, put your best shooter as SG, second best at PG, third best at SF, but I recommend putting your starting SG at starter/backup at the very least to get him as many minutes in game as possible, providing him the time for the shots.