If the Royal bus drops you off at the TTC, walk to the Poly and get a bus to Springs from there. Takes too long to go all the way around to the Contemp for a bus. Coming back from Springs, bus to the Poly and walk back to TTC.
All Disney Transport, especially the monorails, is becoming more and more UNreliable by the day. Factor that in to all transportation times. When on a tight time schedule, Minnie Vans might be the way to go. I would personally never rely on the monorails or Skyliner to get me somewhere in a reasonable amount of time. I do consider myself a bit of an expert on the subject because I used to drive the monorails…