philloitaly, I am also wondering if you are trying to get it in and out of 4 low correctly
Meaning wondering if all the parameters are being met, like park brake on and in park or if a manual trans in neutral and clutch depressed etc.
So, you "can" shift the transfer case manually and it works 4 high to 4 low?
Starting to change my mind and think the case needs to be split and the fork checked / replaced

 

Whole system is disabled..there is a self test every time the vehicle is started, if there is any issue ESOF is completely disabled. No relay click etc. there is a chance if it is in 4x4 at time it continue to display that....but..ive never seen it. It doesnt typically onow where it is, and wouldnt show something . PCM would have code in any case

 

I think you forgot "Keep your foot pressed on the brake while shifting"

 

I allow my truck to roll very slowly while shifting the transfer case but with the trans in neutral, so roll forward or backward on a slight grade while in neutral.

If you go too fast it will warn you to slow down. They recomend the same thing to engage 4Lo so it shouldn't matter when disengaging.

Back in the days of transfer cases with actual chrome shift levers a stuck transfer case could be unstuck by backing up at about 5-10 mph and jamming on the brakes on a dirt surface. The idea is to let the front wheels slide a little which unjams it.

No idea if this will work with a newer F150 or not but if mine was stuck I would try it.