Great then! Maybe we will get to use the buses after all.
Just so everyone knows: my concern is not so much arriving on the parks in as little time as possible. Rather, my concern is being able to wake my daughter up as late as possible. She is fine staying awake late, but I'm afraid that waking her up too early will not turn out well. I am already planning on arriving at the parks late morning. However, what time do I wake her up? So, if a method of travel takes 30 minutes for sure, and another takes 10 minutes, but can have a random wait of up to 40 minutes, I am willing to take the 30 minutes sure one, because it allows me to wake her up later, since there is no need to program buffer time. I have some important FastPasses ending 30 minutes after the time we intend to arrive at the parks (and changing those is either not possible or affects the plan too much), and so I want to make sure that we arrive at the park by a certain time, all the while waking her up as late as possible. I'm willing to pay some cab money if that is what it takes.
From what I gather so far, the best option for MK is bus. It is not only the fastest method, but it also seems to be frequent enough that we are sure to find a bus with a likely wait of no more than 10 minutes.
Now, for the other parks, I gather that HS and EP are frequent too. Now I need to determine if the wait is too random, or if I am likely to get a bus within 10 minutes. Otherwise it seems that a cab may be a better option, because even though it may take slightly longer, it is less random, so no need to program buffer time.
For AK it seems that you had a bad experience, and I read about other people having problems too, so maybe we should get a cab to go there after all.
By the way, I would like to thank you and everyone else helping me out here! Before having a baby I was always at parks at rope drop, and did not care if I had to leave 2 hours in advance to make sure. Now I have to consider sleeping schedules carefully. On top of it I seem to have the opposite problem of most people: my daughter has problems waking up too early, but has no problem staying late. I don't have to worry about coming back to the hotel for naps, leaving the park early, etc., but I do have to worry about getting to the park as late as possible and still get to do the things we want to do.