Hi, Lori! Oh, thanks for the compliment on the panel! Unfortunately, there really is no way of planning around conventions or group events unless you know when a certain group typically hosts events annually at WDW. For instance, there are several grad nights and 8th-grade nights hosted in May and June. However, those are specially ticketed events and wouldn't have much (if any) impact on a family's vacation other than a park being closed a bit earlier on sporadic evenings.
As members of the Moms Panel, we only have access to the information that is given to the general public. I wish I could give you some "insider" tip! However, as a convention attendee at WDW, my husband and I usually attend business conventions in March and May every other year. One is a huge convention of thousands of people, and the other is only a couple hundred. The convention and conference business is a big one at WDW, and I'm sorry that there is no central location where you or I can see when the peak times are for conventions, conferences and special events. My best advice is to plan your vacation as you would and take advantage of resort benefits like the convenience of being on property, WDW transportation and Extra Magic Hours.
Have a wonderful day and a most magical vacation!