If your child doesn't nap in the stroller, they might just get too much "magic" in the parks all day....On your MK day/s, I would not necessarily take my kids back to the room for a nap, but I would take them out of the park, and do something different...like a monorail ride around the MK resorts and back just to get away from the same old atmosphere...maybe stop at one of the resorts and have a quick snack just to see the decorations at the Poly or Contemporary....this would only take an hour or so, and would break up the day.
Our kids (we have 4 and have been going to WDW since our oldest was 18mos), have all been big nappers, so we could not go without an actual nap, and I felt it ate up alot of our day, as well, and we always went during offpeak season, so I just always did ParkHoppers and utilized EMH....but I could nopt stand the thought of being one of those parents/families with whining/crying kids at the end of the day...I also realize that what worked for us might not fit your plans, and your child might not be a big napper (mine took minimum 3 hour naps until they were almost 5, then it was 2 hours)...so I thought an alternative might work better for you.
now, with some older and some still in nap mode, we divide and conquer....
I also sent you a PM...so check that out as well.