If you want to save a great deal of time, hire a taxi.
If you wish to take Disney transportation, when exiting from the front of the park take the monorail. Depending on how long you have to wait for it, allow about 30 minutes travel time. Then you will need to switch to the resort monorail at TTC and ride to the Contemporary. I'd give that another 30 minutes. So an hour each way to be safe. You can switch to the express monorail, get out at MK and walk to the Contemporary but I don't think that would save a great deal of time.
That's the only way to go from the front of Epcot, there is no bus from there to the Contemporary.
From the International Gateway you can walk to the Beach Club, take the bus to MK, and walk to the Contemporary. Again you will need to factor in at least 20 minutes possible wait time for the bus, so give it an hour.
4 hours does sound about right to me: an hour travel time each way, possibly 2 hours at the restaurant.