I would love to help. As this highly depends upon what you are talking about. I will need more info, maybe a video or the attempts you have made for me to help further if possible.
Unfortunately the mesh will get squished regardless, as you’re compressing it down and not compensating for the flare of the liquid that’s sat at the top of the glass. The only approach I could imagine working is having a uniform cylinder with no flared sides that is scaled to the finishing position at the bottom of the glass!
–Hopefully the way I explained it made sense in some way!