To solve this mess, I plan to pour a concrete pad in front of the
door. The problem is I dont see this mud getting really dry anytime
soon. There is still water seeping out the edges of it and running
down the hill next to it.

You need to dig out about 8" of mud, will that get you nearer to solid
ground ? Then lay down some white plastic 3-4" sloping drain pipe either
enclosed in a "sock" or at least covered by draintile paper to keep dirt/mud
out of the pipe. Run it over to the 'hill' you mention where it can dispose
of the water.
After that backfill the excavated area with "road base" or 1" minus gravel
and compact with a roller or plate compactor and THEN you can form up and
pour your concrete on top of the gravel base.