I do know how you feel. I'm not trying to minimize that. I went through the exact same crap a few years ago. But the day I started a very important internship, it needed to stop. I went in for my first day on a day 6 of the peeling cycle, and I was trying to get them to heal by not putting stuff on them and not getting the skin off. At that point, my lips could hardly move. My boss would say something that would make me laugh, but I couldn't spread my lips into a smile. I was being introduced to people like this. It must've looked incredibly strange, and I'm pretty sure my boss was looking at me funny whenever that happened, because I didn't look like that in the interview.
As soon as I got home that day, I smothered Aquaphor all over my lips and let it sit there until I could exfoliate them completely, and I never looked back. I was so much happier and felt so much freer without worrying about them, and frankly I don't care if exfoliating makes it so the condition is harder to heal. I can't deal with the healing process at this point in my life if I have to live with thick, hardened, cracked, discolored lips for a month, if that would even help. So as long as I'm not making it more likely that I'm going to get skin cancer on my lips, which no one seems to know, I'll do this as long as I need to.
You say you have a gap on your lips- does exfoliating them make this gap look worse, or are you just worried about making it bigger? Could it be that the gap is from letting the lips harden, so that's the only place it stretches and therefore you get a big crack in the middle?