my lips have never bled either. I think that is because I got EC in a different way. I was a habitual blixtex DCT user (it has awful things in it like phenol). I would use it up to 7 or 8 times a day sometimes. When i got an allergic reaction on my lips to chapstick (very rare but it happened- they broke out in hives), i had to stop putting all products on my lips to find out what the cause was (later discovered it was the fragrance). From stopping cold turkey my lips went through some sort of withdrawal where the skin started splitting and then i sort of picked at it (so i guess in this way its the same as yours) and then they started the peeling process after continual picking.
I think that the same thing is wrong with me though- no basement membrane. I dont think it matters how we got it but Cheilits Fighter, i definitely think you're onto something. All of this is a little confusing to me too but i'll try to research it at well. Maybe i'll try to head over to the library when i'm not studying for finals lol.