The key component is trying to figure out how to bring parity and compare tournaments to one another, as some tournament scores are high and some are low. The easiest way I can see for it to work is to reset the scores after completion. Let me explain.
For category awards, if the top 4 scores were 178.5, 178.0, 177.5 and 177.0, reset them with the top score moving to 180 for TOY considerations only, as this was the "perfect" score fo the event. Results for that category for category TOY consideraitons would then be
180, 179.5, 179, 178.5 etc.
This would allow a comparison across tournaments as to how you placed versus the other teams, allowing each first place to earn 180 towards their point chase for the category at each event with others being lowered based upon how close they were.
For Overall TOY, you could then modify this to be either out of the 720, or for each event, a summary addition of your total places. The addition could make it the most interesting, as it could reward the teams that cook the most consistent across all four categories with the best shot on an average consideration. Win 4 tournaments but tank in chicken at others? Well the team that got 4 Reserves and 6 other top 5's "could" beat on them on an average across their top 10's.
This could "potentially" really bring in some parity to the individual tournaments as it helps rebaseline scores and allows for teams that compete in big tournaments with narrow margins to not be as penalized or even rewarded for finishing. Not a perfect solution, but imagine the "chase" if we were talking narrow differences and how a placing in Chicken on one week could affect the final standings.