My answer to this might confuse you a bit but, it is what I am doing now. I expose the buildup to things that I know will help remove it. This is with either a long shower or when I brush my teeth. The thing I do more is that I cut the loose skin off with a cuticle cutter (a nail cutter will do but a cuticle cutter is a way more precise instrument for this) and I will leave the stubborn buildup alone. This is important and I hope I didn't forget to mention it. You should never force the buildup off. You can gently rub whatever is willing to come off away but DO NOT tear it off.
I am not using the triamcinolone acetonide that Daniel used, at least, not yet. I kinda persuaded my derm to prescribe it for me. I am using the dental paste version of it that dries the hell out of my lips. However, half of my lips are showing a return in normal skin pigmentation and they DO NOT turn white when exposed to water. So I am currently halfway there and this is just after about a few weeks of using the triamcinolone acetonide and randomly at that. The best time to use the steroid cream is before you go to bed. Then you can use any moisturizer of your choice throughout the day. I use the steroid very randomly so, sometimes I'll use it three times a week, or maybe like once a week. But I always apply it once in a particular day and always before I go to bed.
I do use Bepanthen every now and then, but the one thing I like to use (and this may surprise some people) the most is this:
I absolutely love how this ointment makes my lips feel. I especially love the nice light chamomile scent of it too. I wish I knew about this ointment 20 years ago because I would have used it more often than that stupid medicated Blistex that ironically helped to cause my EC. The calendula ointment also aids in softening up any buildup so that it is easier for it to just fall off effortlessly. It is composed of 10% marigold extract (calendula flowers), and 5% lanolin USP in a petrolatum base.
Some people have reported further irritation when exposed to a lanolin product but, this ointment just works for me and my current state of EC as far as providing a smooth moisturizing barrier for my lips. The Bepanthen also dries out the inner mucosa of my mouth slightly, which is why I don't use it as often. The calendula ointment doesn't seem to do that. Then there is that amazing light smell of chamomile and, I love chamomile.