Hi! Interestingly enough, my husband and I are going the week of the 11-18.
In 2013, we went also the week before President's Day, and I will say that the Friday we had at MK right before PD weekend, yes, crowds were pretty large. However, it really was the only day that we noticed an uptick. But for the days earlier in the week, we did everything we wanted to do in the parks. We did three days at MK, so it certainly enabled us to get multiple rides. I remember that we were able to walk on Pirates, Haunted Mansion, the Little Mermaid. Even without FP, we were able to get on Big Thunder Mountain and Space Mountain in 30 minutes. Of course, we did rope drop every morning, and so a lot was accomplished then, especially at MK. For parades and fireworks early in the week, we could find great spots even 15 minutes before show time. By Friday, though, it was a good hour wait for Wishes if you wanted a prime spot.
So will the week of 4-11 have lighter crowds than the 11-18. Yeah, I'm sure, but the 11-18 will still be very manageable for you.