We just did this tour on 12/13. Monorail definitely sounds like the best option for you, but double-check the times. We were staying at AKL so we got a cab to take us to the Contemporary. We had checked with the concierge at the Contemporary the day before about monorail times and he couldn't guarantee us that it'd be running that early. So to be safe, we had the cab driver drop us off at the back of the contemporary parking lot (farthest away from the resort) and walked the path to MK.
Side note - we were paranoid about being on time. One member of my party is an extremely slow walker. So we left AKL SUPER early. And of course, nothing took as long as we had thought...and we ended up being at the entrance before anyone was ready to let people in! Chatted with some maintenance workers in the parking lot for awhile. A couple of security guys came walking by with their cups of coffee and felt bad for having a drink in front of guests. (We assured them it was fine!). They opened up a bag check line for us and even wiped down a bench that was still wet so we'd have a place to sit. We just sat quietly, watching the park open up and it was FASCINATING! Heard sound checks of the sound system, saw lighting effect checks, watched how they prep the entrance for guests. It was VERY cool.
And the tour was FABULOUS. (This from a girl who likes trains well enough, but wouldn't call herself a FAN of them...) Seriously. LOVED it. If you have Jimmy as your tour guide, tell him there's a family in Ohio still talking about the fantastic job he did!