We usually do the very end of Jan/ first couple of days in Feb., too. This year we went MLK week. Arrived the Sat. two days before MLK day, stayed till the next Sat. a.m. It was definitely more crowded but it was certainly manageable. We did OK as long as we had a plan together to hit popular rides first and used FP wisely.
The best way to figure out how early MLK week guests might show up is to look at school schedules from all over, especially the East Coast.
Last year our schools had off the Friday before and the Monday of MLK day. This year we just have Monday off, meaning less people (from our County) would vacation the week prior.
When looking for the optimal time to plan my trip, if we have several choices,
I just randomly look up websites for school systems in several states and see if there is any kind of pattern to which days lots of districts have days off.
Or, just pick the time thhat works best for your family, and go with a well-planned itineary.