You can be in the Animal Kingdom parking lot in 6 or 7 minutes using Sherberth Rd.
DHS: in the parking lot in about the same time using 192 and World Dr. It may be a little longer using Sherberth because you end up going in the back entrance to DHS.
MK: you can be in the parking lot in about 12-15 minutes but then you have to either walk or take the tram to the TTC, then the ferry boat or monorail to the entrance. If you want to make rope drop then allow 45 minutes from WH just in case you have to wait for a tram or monorail.
Epcot: in the parking lot in 12 - 15 min.