You have a few options, and the monorail is definitely one. You would take the monorail form the front gates of Epcot to the TTC, then change to the express monorail to get to MK. It's probably faster than any bus.
Should you find yourself at the back of Epcot, near the International Gateway, you could exit to the Epcot resort area, then walk to Yacht Club and pick up an MK bus from there. This bus route will probably make a few stops (don't know the exact routes for these resorts but buses can stop at multiple resorts), but it will take you directly to MK, bypassing the TTC. If you factor in walking across Epcot (which is pretty large) then this could be the easier option, though it may or may not be quicker.
ETR: Some incorrect information. Thanks, Robo.
Give yourself plenty of time either way. I recommend budgeting an hour for transportation, though it likely will not take quite so long.
ETA: You can also just take a bus from the front of Epcot to the Contemporary, then walk to MK or ride the monorail. Also, you could bus to the Grand Floridian or Poly and take the Monorail. If I was at the front of Epcot though, I'd probably just monorail it.
Sorry, but (unless the monorail system is not operating for some reason)
there are no buses between any of the MK Monorail resorts (CR, GF, Poly) and Epcot.
Sorry, but (unless the monorail system is not operating for some reason)
there are no buses between any of the MK Monorail resorts (CR, GF, Poly) and Epcot.
This will require a stop at a resort. Really, you can bus to any resort and then bus to DS. You can also bus to Port Orleans, Old Key West, or Saratoga Srpings and catch a boat to DS. You can walk from Saratoga Springs to DS as well. Allow a lot of time for this one as DS is a long haul from AK.
One detail that you left out is are you driving your own vehicle to Epcot? If so, it might be better to drive from Epcot to the MK parking lot at the TTC. Especially if you are staying at the MK until the party is over at midnight, there may not be any transportation back to the Epcot lot.
There are no buses directly from Disney Springs to/from the parks. The fastest way would be a taxi/uber from AK. You could also take the bus from AK to AKL Jambo House and hop on the Disney Springs bus there. You could also catch it at AKL - Kidani (same bus). The Disney Springs bus for the AK resorts stops at Jambo first and then Kidani and then heads to Disney Springs.
The way I would do AK to Disney Springs is bus to Saratoga Springs Congress stop and walk over to the marketplace area.If you're planning on going over to the west side area and its still light out(the golf course is dark) I get off at the Springs bus stop and walk over through the pool and golf course over to Disney Springs,not as easy as the walk from Congress area to the marketplace but sometimes I feel adventurous.