A better idea would be to have each team run together on the course at staggered intervals. They all train together anyways. It would be a great team sport.
This is what the league is talking about where I coach. They're also talking about limiting jv and f/s races to only 7 teammates, or even eliminating JV from races, so each team brings 28 or 42 people at the most from the two genders. With chip timing, its quick for them to run multiple races with each team starting a minute or so apart.