Are you doing the train tour at the MK? When we booked that tour, we were told to park at the Contemporary. We just told the guard at the shack and he was very accommodating.
It's so early, it's not likely a regular park visitor is going to be trying to park in that lot that early in the morning and then just hang around for hours.
Just call the tours desk back and ask them what's the best choice for you. I would not count on taking the boat. The monorail maybe, if you're really that uncomfortable about the CR, but don't wait on the boat that early. They may wait until it fills up and your tour won't wait on you.