As someone with short heel girth (the circumference of my foot from the front of my ankle to the farthest back point of my heel is very small compared to average) who is also very mobile through that joint- heel lift is my nemesis in all boot fits and is a particular hurdle in touring boots. Ultimately, I think you want to work with a good boot fitter to resolve (and play with your buckle microadjustments and form as mentioned) but I wanted to give you some reassurance that you could be in the right boot for you as I tried on every touring boot in my shop and went with the Zero G as having the best out of the box heel hold. That + a custom footbed was all I needed to make the boot work for me. A custom or semi custom footbed can help your foot hold the optimal position inside your liner and shell by taking up the appropriate amount of space under your arch and forefoot.
When I sweat, I can still work my heel up so I am mindful both of seating my heel in the liner and the liner in the boot before starting to skin or ski and resetting it a couple times on the ascent - I'm in VT though so my ups are shorter than yours

. Your liners should have come with laces which can also help cinch down the liner around your ankle - I'd rather have the friction be from liner to shell than between my foot/sock and the liner, if that makes sense. I also cinch my power strap down directly on the liner, inside the shell for more hold because I also have skinny calves
Hope you find a good solution! Keep us posted.