I started using Total Men's Primary care. I see a PA most times I go, but I think they have docs available also? I used to use ARC Far West and in Cedar Park, but struggled with much of the same things you are, especially with appointments being weeks out, and a buddy told me about TMPC. I would recommend them, if they fit your needs.
At TMPC, I made an appt online that morning for the same day, showed up at the location at my time, after they called me to confirm, and was in and out, even as a new patient in less than 45 minutes total. They have a computer you use when you arrive, to fill out your new patient paperwork, which speeds things up nicely as you don't have to hand-write it, and then wait for someone to key it in.
From what I have seen and my buddy agrees, they are running a practice in a modern/efficient manner, unlike 99% of the other places I have been to in Austin in my lifetime. They doc that comes in to see you, and the nurse, are taking notes on tablets, not paper, so that is more efficient also.
I am also like you. I go in every few years at best and don't want to spend a lot of time dealing with failed mass medical practice logistics when I do go. HTH!
Class of '93 - proud Dad of a '22 grad and a '26 student!