Many people with cheilitis control their symptoms by using vaseline and exfoliation. Check the last 5 years of the forum - it's a common method.
That's not to say that it wasn't good of you to post your story yesterday - this forum could use more earnest participants with different experiences and points of view.
I used vaseline for 20+ years and loved it, but I stopped last year when I realized it was only harming my lips in the long run, because it doesn't allow the skin to breathe. It's made from crude oil, and the more I read about it, the more I didn't want to use it.
Vaseline/petroleum is in many products, though - it's hard to avoid. I had to toss some of my body lotions, face lotions, lipsticks, lip balms, etc.
Your exfoliation twice a day is not allowing the skin to heal, it's just tearing down the healing that the skin is trying to do. For the short term, this might look better to people who are looking at you, but in the long term, it's my personal opinion that you are probably harming your lips.
I would not want to manually take my skin down to a raw layer over and over - it is probably causing a constant healing crisis rather than stopping the cheilitis process.
Areas of the body that have cells that undergo a lot of rapid turnover for extended periods of time are more prone to get cancer, because of the greater age and higher mutation rate of those cells.
The bottom lip is also often exposed to a lot of sunlight, and is a typical place for cancer to develop anyway.