Not sure what time your reservation is for, or are you wanting to try and ride ROTR as well? I believe the skyliner is running from 9am to 8:30pm, so that might not leave you enough time. Would be the funnest way though, (in my opinion). You could take the skyliner to Epcot, (gets off very close to the YC), and then walk to HS from there.
We were looking at 7:30 breakfast reservations in order to have plenty of time to eat and then walk over to HS. So, we would definitely need to taxi or Uber, but that's not a big deal. We definitely want to be at HS as early as possible. It looks like people are able to line up to start getting into HS around 9am or so?