I have a similar problem to you. Playing DPS in this game sometimes leads to me just being overwhelmed, whereas with healer if I start to feel overloaded I can step back and focus on just watching health bars and breathe for a second. It was especially overwhelming when I went from the fairly basic level 50 rotations to Heavensward piling on a lot of stuff. A very strange feeling coming from WoW where for the longest time I was exclusively a DPS.

The two jobs I have found simplest to play are BRD and RDM. Both feel fairly cyclical to play. I'm far from a pro on either of these, but outside of the opener BRD feels less overwhelming and I'm just occasionally looking for procs. And RDM doesn't change rotation too much while being simple.

I'll echo the others above that muscle memory plays a big role so that you're not staring at your buttons trying to remember. Also I have found that my UI is important. Making sure things like my gauge, important buttons, and health bars were in a location that I could easily see without having to glance away from AoEs all the time really helped with my ability to manage both DPS and dodging. It's all down to practice, though, I think.