I think it should still be a snake draft however keeping 3 players in a 12 player league with 13 roster spots seems like a bit much. I think keeping 2 players would be a bit more fair and is more logical for the type of league you're in.

However, if this cannot be changed, I actually prefer drafting in the same spot for the whole draft. Your league won't last long if the good teams get to keep the best players for multiple years.

There has to be some balance here, and I think while using the "same spot" technique may give a greater advantage to the worser teams, using the snake draft and allowing 3 keepers won't keep this league competitive.