You can enter EPCOT via IG at rope drop. They just simply direct you in the direction of Future World. You can not roam around the World Showcase. I love the EPCOT resorts personally.
But like stated above, each resort is closest from some parks and further away from others.
As for walking through EPCOT to hit the Monorail, I would not recommend it. We did it one time because the kids wanted to ride the monorail. I am convinced it was much longer than waiting for the bus (one has to walk through EPCOT, get it line for the Monorail, wwait for the monorail, go the TTC, get of and then wait for another monorail to MK).