I did it something very similar as a as a solo traveler very early January 2015. Crowd level was probably about a 4-5 with the end of the Christmas rush. DAK had EE in the morning so that helped me out that that park. MK closed at Midnight.
DAK rode Safari, Everest, and Dinosaur
Took Bus to DHS
DHS rode TSMM (FP+), GMR, TOT (FP+), Muppetvision, Star Tours (FP+) & Early 11:20 or so lunch at ABC Commissary.
Boat to EPCOT
EPCOT Rode Imagination and Spaceship Earth (Originally had plans for Nemo and/or Mission Space but had a hard deadline of 3:00 to get to MK because I wanted to watch the parade.
MK rode a ton of "classic" attractions in addition to watching both parades and fireworks.
Rode Jungle Cruise, Pirates, Splash Mountain, Country Bears, Tiki room, IASW, Peter Pan, Haunted Mansion, Pooh, 7DMT, Buzz, met talking Mickey, Rail Road and I'm sure several others.
For me, the "hardest" part was deciding when to make my FP+ for at DHS. Make them too early and they are going to expire. Make them too late and you're killing time. Like other's have said, right now you've got 3 tier 1 FP+ you can only choose 1. I would keep TSMM and make 2 tier 3 of your choice. You "should" be able to squeeze GMR in between 2 FP return times the same with RnR especially if you use Single Rider.
Second, at least when I was there a little over a year ago, there is a FP+ machine at the international gateway. But, at least the time I arrived the sun was shining and completing washing out the screen.
In the MK, try to make a FP+ as soon as you can after entering. With your FP's you may need to decide between quantity of attractions and quality of attractions. I went for quantity of attractions and pick the closest "reasonable" attraction in time. So, I picked the HM's and Pirates, and Pooh's who's window started in 20 minutes over the Space Mountain who's window didn't start until say 11:00. In between FP+ I filled first high capacity attraction (tiki room, People Movers etc.) as the evening moves on, in your case especially during EMH, build to the headliners. My original goal was to do 7dmt last but the line was not as long as posted so I was able to slip over and walk until Peter Pan right before closing catching the at the time new "interactive" queue.
Lastly, if your goal is RD at DAK to the end of EMH at MK, plan some in park "downtime" Try and relax on the boat ride between DHS and EPCOT, take a break and watch the tiki birds etc. Have fun.
Otherwise I would have totally done the same order as you. Our challenge was at least 2 attractions (we did three in most parks) and one food item from each park. We are talking about doing it again and adding in Disney Springs in April because it was actually easier than we thought it would be. We used all WDW transportation like you are suggesting.
