Just spit ballin here. Posting what I just did and then experienced.
I put my index and middle fingers on the side of my jaw. I set my jaw to make a wide open “ahh” vowel. I could feel my jaw muscles tensing when I started singing. So I massaged them while singing and got them to relax. I would sing a song only on the “ahh” or “ehh” vowel shape but would then use only my lips to change that sound (no tongue. trying to disconnect the tongue from the lips, too. the tongue does have to move to make an “ehh” but that is ok here). It forced me to feel relaxation, even if only for a brief second, and then holding the relaxation. It took a lot of mental gymnastics to get all the unnecessary movement to stop.
So, singing as many sounds as you can make in one position really forced me to use my lips.
Yes indeed, here’s the basis for trying your piece with no consonants. When it comes down to it, every vowel is just a modified ah vowel so if you have that as your basis, breathe the vowel on your in breath, so much that at first it’s actually audible, you’ll have the perfect preparation for that all vowel singing!