Yeah, May before Memorial Day is the best.
We go to WDW 4-6 times a year and have lots of experience staying onsite throughout the year.
Even on a good day, January is in the high 70s during the warmest part of the day. Mornings and evenings can be downright cool - jacket weather. And you can get the odd 50-degree high day in January. Who wants to be at WDW with that kind of weather?
May is hot, usually in the high 80s or low 90s. But summer humidity usually hasn’t hit yet. This means you will sweat a lot in the sun but feel noticeably more comfortable in the shade. We find ourselves hopping from shaded spot to shaded spot, and usually do well at the theme parks.
Crowds are more modest in early January (excluding the marathons or MLK weekend) and in May (before Memorial Day). I’m not sure either has the advantage here.
We don’t go to WDW to wear jackets. We go to wear shorts and swim at the pool every day. For us, it’s May all the way.