So we are beginning the process of building and wanted to try to time things where the completion of the new home would coincide sometime in May, June, or July so we could list our existing home at that time with the thinking being that it is the best time to sell given we are in a great school district.

Is that thinking overrated given there is also more inventory at that time? Other than the holidays, do homes move as good (or almost as good) in the spring and fall as they do in the summer?

My personal rule of thumb is never sell between Nov-Jan as those are the slowest months every year

I think it's kinda a wash. Less buyers but less supply. Ive actually seen research that shows January is the best month to list in the south, for getting the best price. Weather isn't an issue. People come out of the holidays ready to get stuff done but find a limited supply.

Depends on where you are located. In some parts of the country because of weather there are times that it becomes REALLY slow. In all areas there are busy and slowER times, but as mentioned above there is also less competition in the slower times. There are many factors to consider. Most Sellers have reasons that make one time or another better because of other factors. If the factors are the same in every month, and you truly could choose based only on better times of year, I'd say April-early August would be ideal in my market. But again, there are always other factors in my experience...