AST main so I have no problems with sage and the target switching is pretty standard for any healer once you are a bit more competent. Just take a breath and practice flicking between mob and player, you can also keybind to target your target's target for even easier and faster flicking!
Sage has a lot of forgiving qualities too it imo since it has a lot of insta cast heals to allow for even easier ogcd usage and movement. I would also suggest taking a proper look at your skill tooltips, a lot of your ogcd's give a bonus 10% dmg mitigation as well. Always in dungeons aim (if dps and tank are competent) to heal solely with ogcd once you are comfortable on the job.
AST's old sleeve draw was very busy and I loved it, I enjoy sage for not feeling like I have nothing to do as well. You just need to relax a bit and practice.