Lbinns, if you are still here, could you possibly try and remember how long since changing to that toothpaste did the lips mostly heal up ?
I have had a look at the ingredients and it is not a food grade toothpaste. Let's float the possibility that it's not the contact of the toothpaste on our lips causing the irritation, it's the ingestion of small amounts of paste when brushing.
What is to say that the irritation of the lip lining is not as a result of irritation of the gut lining from toxins within the paste. OR BOTH.
Besides the aquaphor/mositure method I'm currently trialing, I'm considering going back to a food grade toothpaste I purchased some months ago and giving it a longer trial of 6-8 months instead of a few weeks, as per last time.