I've been in similar situations where most people were waiting on a particular letter, but the most winners I've ever seen at once is around 25.
I show the probability of going 44 calls and avoiding any one letter (not just G) is 1 in 1,517,276. Here is a formula to that probability: 5*combin(60,44)/combin(75,44) - combin(5,2)*combin(45,44)/combin(75,44)