My 2011 with 95000 is doing the same stumbling issues at random and sometime goes into a full limp mode missing on multiple cylinders and the wrench symbols pops up but no DTC codes on my sct so it's a little different than you situation but mine also just started in the last few weeks. The wired thing is if I shut the truck all the way off its like it resets because it will run fine and Ford can't pull any codes at that point either ...none are saved on the computer.
Seems like a stupid answer but I think I got dirt or debris in my fuel tank. It seem to happen when I'm low on fuel. And the reset seems to come from the fuel pump turning off and losing pressure and in turn washing out the screen on the pickup
I know it's not exactly the same with no codes but otherwise sounds the same.