I agree, 15-20 minutes is good for EE . You might want to add at least 5-10 minutes more for non-EE days.
Last Thursday, we got to the Mickey and Friends parking lot around 6:32. We got parked and on the tram very fast. I think we were at the gates around 6:40 and ended up being the first guest through the castle (the majority of the guests went towards Space Mountain). On Sat. we arrive a few minutes later, perhaps around 6:45 (we stayed on-site, so had EE again). We were pretty close to the front and got in quickly.
My recommendations -- Don't go to Space first. It takes up lots of time and everybody else was going there. Use FP later, or go after you do other rides after the first rush. We did SM on Sat at around 7:40 with around a 5 minute wait. I recommend Peter first, since it backs up quick.