Doodle.com is a great website for coordinating meetups with busy people. I have used it for planning parties and business meetings. I am particularly a fan of coordinating in a way that reveals as much information as possible. Doodle.com does this for me.
Essentially what you do is create the details for the event and all of the days and times that are potential options for meeting up. You then send the link out to all the participants and they mark their availability. I usually enable the middling response of yellow. This is equivalent to the phrase "if need be." You can then maximize your meeting by picking the best time for all the people.
Unfortunately the free version does not have calendar integration so if you aren't up for spending money on it you'll then have to contact all those folks again and inform them of your response. I think this is fine though. They have to make their money somehow.