Here is our defensive approach for who gets priority on a flyballs in the seams--50/50 balls--that threaten to land in between an infielder and an outfielder.
1. Our infielders are strongly, repeatedly instructed that they have 100% priority on 50/50 balls.
2. Our outfielders are strongly, repeatedly instructed to pursue 50/50 balls aggressively, but that they have 100% responsibility for collision avoidance.
In my experience, this black-and-white approach on 50/50 balls increases catches while reducing the chance of collision.
Again, with this system, the instructions to IFs and OFs must be strong and must be repeated multiple times during the season. If not, you're jeopardizing the health of your infielders.
I don't like gray areas.
Game7, interesting approach. In many areas, there are more than one ways to coach successfully. For me personally, I can't buy into your #1 but I really like the added emphasis on #2 (particularly making them responsible for collision avoidance) and, just as important, your statement that instruction must be strong and must be repeated multiple times during the season.
I can't buy into #1 because I am 100% sure that the reason the traditional teach is for OF's to have priority is correct - fly balls are much easier to catch coming in than going out and catching over the shoulder or something close to it.
This game situation in general is difficult in many ways. It is difficult because the consequences with failure (or even a successful catch) are potentially more significant. It is more difficult to practice (you have to be really good with a fungo to have a high success rate where each rep is a last second call on who will take it). It is difficult to devote the time necessary to a situation that doesn't seem to come up more than once or twice a game. And, Real Green, to address your comment, how do you coach timing when the occurrences that are difficult don't allow for timing? Sure, you coach "call it as soon as you know you can get it", but the reps in question are the ones where you don't know until last second or never really do know. And, no one is OK with the direction to let it drop if it's last second.
For heavy reps, I used to take a tennis racquet and tennis balls out around the perimeter of the mound and shoot reps left and right alternately with two guys at each position (at least up the middle). Some years, we had a guy that was actually that good with the fungo, but not usually. Tons of reps with guys in the right positions affords familiarity with language, timing, speed and abilities. When a player at a particular position is better/faster, they tend to take charge and call it earlier - so you don't have to change the proper teach to account for this. When you work it a lot, it often makes the tough ones look easy and the casual observer has no idea what a disaster the play could have been otherwise. I do think instructing the "collision control responsibility" emphasis is a great one to add. I have also put some responsibility on the SS or CF (when they are not directly involved) to help steer traffic.