If you were to walk to Epcot, it would be about 8-10 mins to the Intl Gateway from S/D. Go through bag check and turnstiles....another 5 mins. Walk to the front of Epcot..about 20 mins. I have made it in about 17 mins but I was moving quickly. You will be going against the stream of people.
Then, it can take 15 mins or so for the monorail to get there, then 10 mins to get to TTC. Then, either walk to the Polynesian from TTC, about 10 mins via the pathway, or transfer to the resort monorail...again, could be about 10 mins. If headed to the CR, stay on the resort monorail until you get to CR, takes about 20 mins or so. Or, take the express monorail to MK and walk to the CR, about 8 mins walk on top of the wait/ride on monorail.
If it were me...I would take the bus to MK from the S/D. Then, either walk to the CR, via the sidewalk that runs directly underneath the monorail line. Or, take the monorail or boat to the Polynesian. Depends on where you decide to eat.
But, I would never walk through Epcot just to take the monorail to the TTC...way too much work and time.