For Magic Kingdom: We left walked out of our rooms around 7:20am for an 8am MK opening day. We took the monorail and were standing outside of the touchpoints by 7:40. I think allowing for 30 minutes total travel time gives you more than ample time. For other trips to/from MK, we used both the monorail and the boat. The boat is a dream. We waited very little for boats (both directions) and it's a quick ride. It's also kind of nice to be out in the open air when you've been surrounding by crowds. The boat is direct to MK on the trip out, but stops at GF first on the return to Poly. It's still a quick ride.
For Epcot: The ride to Epcot is short, but the bag check lines are long. You can take the resort loop monorail straight from Poly to the TTC and then switch to the Epcot monorail line. OR, you can walk to the TTC from Poly (a very short, easy walk) and then get straight on the Epcot monorail. One thing to know is that the bag check at TTC is LONG around park open, so it may actually be faster to take the monorail resort loop and transfer at TTC. Then you have bag check AGAIN at Epcot, which is also long at opening. I'd allow 45 minutes for Epcot due to bag checks.
For DHS and Animal Kingdom: We quickly figured out that we much preferred taking a Taxi or Uber to these locations during the morning rush. Though people here will tell you that buses start running around 6:30am, the first bus to DHS on our park day didn't arrive to Poly until 7:40am. We had an 8am ADR, which forced us to go with a Taxi and it ended up being a great move. The DHS taxi stop is a bit of a walk to the park entrance, though. If you opt for a Taxi, it will be $20 (after tip) and you need only 15 minutes from the time you walk out of your room until you're there. AK is about the same price/time for a Taxi, though the taxi stop is right in front of the park entrance, which is nice. We did see more AK park buses early in the morning than DHS while we were there.
