If competitions were 1 or 2 days you would get a lot more people. That's ORA (1 day) and NSCC (2 days for service, max!).
I don't see a reason for 4 relays. Go with 2. The run down at the end always has the shooters 100m from the butts. The so called waiting relay becomes a complete waste, and sure enough there is always some fng who is not ready even after he has had 30mins. Plus the 2nd man in the butts is a waste. You don't have to score right after the target comes down - put it away and wait till the end to score them all.
It would slightly increase the time between each match, maybe a minute to put down a target and get the new one, as there is only 1 guy in the butts per target. And you would have to give the new shooting relay a 5 min prep time once they walk back. But you would cut the entire time down for the competitions in half! Plus you could really kill two birds by having the butts practice at the same time as the shooter prep. Imagine concurrent activity!
All you need is more target bays. I've never seen anyone shoot besides us in 7 years at Connaught. This should be easy.
You also need shooters/butts to take more responsibility for themselves and be ready to go and take it seriously for this shorter duration.
Unfortunately some rifle teams use matches as first chance of training. Yeah i get budgets are tight, but run some dry runs the night or week before.