If you are staying onsite - you can stay anytime you want. We went in Mid July when it was PACKED, but with FOTL, we never waited more than 10 minutes. The exception to this may be Christmas week - I wouldn't go anywhere near Florida during that week.
If you stay offsite, I would go during a traditionally slow time like early Dec. or mid - late January, May, and possibly Sept.
Late August is good. The weather is still very hot/humid, but the crowds start reducing. Since most FL schools start in mid-late August, you'll be fine. Park hours are often around 9-7, so crowds will be around 30 minute maximums.
Like DM stated, late August is a great time to visit! We were there the last week in August last year and it was a ghost town! I did miss the crowds, I know sounds silly but I did! Just seemed like something was missing.
Then go during Oct or May. Though they are part of the "off-peak" season, they can be very busy months. I call them "off-peak peak" months. This Oct has been the busiest I've seen in a while, and it's not even at the halfway point!