Wow, I'd say that you have beyond-sensitive skin. Mine is sensitive, to the point where I usually shave every other day (my job permits this), but nothing like what you describe. At all.

You'll probably get a bunch of "it's not the equipment, it's the operator" comments, which may be true in some cases but certainly not in all. If you believe technique/prep is not an issue (too much pressure, etc) then I'd say you are just one of the unlucky few whose face just can't take the rigours of shaving. Then I'd say you might want to see a dermatologist, but I'm assuming you've taken that route already since you have stated a specific condition (keratosis pilarus).

If your job allows it perhaps try shaving every other day, or every two days or once a week or whatever it takes. But as a daily event it doesn't sound like it's worth the pain