I hate to say it but the chances of you ever ridding yourself of this condition while constantly picking at it are slim. My advice is to only remove what can easily come off with no force whatsoever, and trim then edges one they become completely detached (not partially!). Moisturize using something that will provide a somewhat thick barrier: calandula or aquafor work for me.
You can get by you're entire life removing the buildup and moisturizing but, in my opinion, the only chance at healing this curse is by leaving the "scabs" intact.
Note: This is something I do, which I would advise against. Sometimes after I shower I gently scrape a sterilized blade over any thick "scab" on my lips and remove the top layer, leaving a thinner layer of dead skin my lips. I wouldn't do it enough to reach the surface level but I don't see any benefit in having the buildup so excessive. The only thing potentially helping is the current (bottom) layer.