I'm sorry I can't help you with escalators.
I have balance/vertigo issues so can not use them at all.
I have problems with lifts as well but not as bad as stairs and escalators. Makes life very restricting unfortunately.

What is the worst part? Is it anxiety or is it balance or both?

I imagine that a really crowded or an empty escalator would be problematic.
I have seen tips for young children getting on them to hold firmly on the sides and swing feet at the same time onto the top step but that may not be so easy for an older teen or an adult.
Standing close to one side and holding one side only may help as well. The problem with that is that sometimes the railing moves faster than the escalator.