Hi,
we've stayed at the Davey Crockett and done character breakfasts a few times, you just have be creative with car parking

We managed to go to the early sittings and park in the best spots in the car park. When you go for your breakfast drive towards the
Disneyland hotel, the turn off is right beside the turning for the station, and tell the person on security that you have a character breakfast booked. We were let into the car park, which is where the cast mambers park I think, and it is down the side of the normal car park, and you can drive right to the front and stay there all day.
The sittings were about 7.30/8 and 9am when we went last. They last as long as you want to stay and eat, but we usually only stayed until the characters had been round and the kids were finished eating, about 45 minutes maybe. We always go to the first one so we can go to the parks when they open.
Try ringing the Disney travel people or getting a copy of the actual Disney brochure for DLP, you can get the sittings from them.
Hope this helps.