Typical softball configuration is F3 in 30-40 feet from plate, but only a step off the baseline, and F4 playing normal position, but covers first on bunts - most teams have F3 play bunts down the first baseline, throwing to F4 who is covering first no matter who plays the bunt. My scenario is a hybrid of that, just shifting F3 over about five steps, covering off "no man's land" in between the rubber and 1B, then shifting F4 to cover the gap now made down the line. Since F4 typically covers first on bunts, receiving the throw is nothing new. The bigger glove gives F3 a bit of an advantage in that position, especially since quick reaction becomes more relevant, and simply knocking the ball down becomes more important. If you can just stop the ball you typically have time to throw out the runner.
Having said that, I have ALSO done as you suggest, and switched F3 with F4 on standard bunting at bats, putting F4 about 30-40 feet from the plate, on the line, and then moving F3 over to where F4 normally plays, having F4 play the bunt/slap, as the better fielder, and F3 to cover first, as the better receiver. The other advantage here is if the batter does actually hit the ball, and hit it to F3, my F4 is fast enough (at least much faster than F3) to get back to first base. And, funny enough, I have also had coaches try to complain about that configuration, saying that my player is playing second base with a first baseman's glove.
In either scenario, at the time of the pitch, F4 is closer to first base than F3, but F3 is wearing the trapper. But I have yet to find anything in the rules that says that the person with the trapper must be the person closest to first base. Not that it matter's who's closest. I've seen games where putouts are scored 3-4, 2-4, 1-4, or 5-4 eight or more times in seven innings, and F3 only gets a couple of putouts. Who's really playing first base?