Offer two or three specific windows and ask people to pick, rather than asking when they're free. Open-ended availability questions produce vague answers and endless follow-ups; a short list of real options gets a decision in a day.
Asked openly, most people answer with a hedge — "probably most of June?" — which isn't a commitment and can't be booked against. Asked to choose between the 12th–19th and the 3rd–10th, the same person gives you a real answer.
There's usually one. Decide early whether the trip waits for them or goes ahead — and tell them that's the situation, kindly and clearly. A group of five that books beats a group of seven that never does.