From personal experience:
Medical Overflow parking at DHS is very close to the entrance. They have a couple of different areas they use for this. One of them is really close.
At Epcot, it's very close as well. Depending on how crowded the area is, you may actually be closer that the HC area.
At AK, it's relatively close, but still a bit of a walk. Still closer than regular parking.
At MK, it's horrible. Not close at all. It's at the far end of the front lot, then you have to go down thru the tunnel and back up just to get to security at TTC. Then finally you get on the ferry or monorail. It's really a pain to park at MK. If recommend using the guest drop off, then go back and park in the lot.
Steve