Here's a 5:04 with a crude Doc Alice route I tried. This could potentially be cut down a good deal if there were any way to consistently guarantee pardner location unlocks.

Interesting things about the route:
-Seems slightly more consistent because there are two routes for wandering: Silversmith/Stearn's Ranch and Silversmith/Buttonwillow, in either order, rather than depending on getting a first try Silversmith.
-Buttonwillow carries a random amount of needles.
-There's probably a fast Military Cemetery and fast Buffalo Pile if we can find the shortest route for talking to the pardner in each area.
-It's probably worth trying to talk to Doc Alice while getting the turnip plated to try getting a Fort Alldead unlock, to allow the run to skip Fort Memoriam and the fudge.
-Run should only really need 5005 meat to finish.