If ours fell asleep in the strollers, we stayed in the parks. If they were that exhausted, nothing was going to wake them up. One of them even continued to nap when we were in Mama Melrose.
We used the time to shop, sit and have a Gran Marnier orange slushie, get a/c on a hot, summer day, sit on a bench and relax, whatever.
We never walked to the front of the parks, walked to the bus, waited for the bus, got a sleeping kid out of the stroller to pack it up, went for a bus ride, opened the stroller, put a (hopefully still) sleeping kid back in the stroller, walk to the room and put the kid in bed for a nap - and then spend the time going back to the park.