Not sure if it’s usual to do this, but I usually put something underneath of them (VEEEERY) carefully. This (in my mind, at least) helps reduce the risk of them falling during the molt. There are a few prerequisites to this, such as:
1. They are not molting on something that moves if you open the container.
2. They are VERY sturdily attaches to the surface they are on
3. They are not immediately above anything that they can fall on to.
I have been doing this for a few years, and I have never had a mismolt, as long as the humidity/temperature requirements are met.
Heres a pic of my newly L6 female, who molted today:
the perspective might make it a little hard to see, but the egg carton is about two inches below her, just in case she fell. She didn’t fall, but it is definitely a good precaution I usually take.
Obviously the most important thing is just the surface they grip on to. I think it is definitely good that you upgraded the mesh, since that’s usually what they hang on. Just make sure it is stretched tight, and it doesn’t sag when she hangs on it.