After enlarging the picture, it sure looks like there isn't much drop from door and out 4'. Then it looks almost like there is a very shallow bowl area. (only way I can describe) I'm not sure any solution is permanent without addressing drainage.
That's indeed what has happened over time. The general grade doesn't really have any noticeable hollow there, but the ruts do have a deep spot about 8 feet out from the door. This may be more from me stopping the tractor there to hop off and open the doors every day, than anything else. But yes, whatever I do for stability, I'll also be making sure the grade is continuously sloping away from the doorway.
I did a quick mock-up of my concept, for pour-in-place, just to get a sense of how much material it would require.
That there represents 1.55 yd3 of concrete. That'd be 93x 60-lb. bags of QuikCrete, or one very small load of ready-mix. Another compromise would be to have 1 yard of sand and 1.5 yard of aggregate delivered from the supply house right down the road, and then just cart home a dozen 94 lb. bags of Portland, to mix myself.
I'm leaning toward forming and pouring myself, both because I think it will be a heck of a lot cheaper (purchased lintels would be $4800), and because I think it will be easier to get it all level and plumb with a single 100 lb. form, versus placing 24 individual 200 lb. purhcased plinths.
I have a guy working here early this summer, replacing a walkway and repairing a retaining wall. I may just get this excavated and formed myself, and then let him handle or help me with the pour.