So I apologize that this question is a little off topic (but related)...but when is the best time for someone to go to a.) go in a slow season AND b.) avoid lots of large tour groups?
I used to like the end of January but when we went last year (2013) we ran into so, so, so many tour groups. I wasn't too upset by behavior other than they just traveled in large groups so that you couldn't get around them and the lines and FP's and even just sidewalks were so congested it made the parks miserable. Overall I'm sure crowd levels were low but we had to leave Epcot one night because we had to pass at least 4 tour groups that had at least 50 people in it each and you'd run into one after the other and you couldn't walk because if a group stopped the whole sidewalk was like a parking lot.
I think your best bet would be to go during the second week of September. I believe that is one of the slowest weeks of the year as schools are back in session. I would also suggest the first 2 weeks of November if you want better weather than September which is still extremely hot and humid.
We went to WDW the last week of July @ 5 years ago, and the tour groups were everywhere! It totally turned us off to ever touring in July again.