I will personally say that my specialty, as my name indicates, is a great match for many of the things that you are looking for. The better than avg schedule, laid back feel, non-urgency of most pts./consults, etc. is one of the reasons I switched from rads which was hyperintense to PMR. It has gotten quite a bit more competitive in the past few years, but still manageable. You can find good gigs out there, and there are many things you can do within the field, which is nice. It also allows the potential for more admin type stuff in the future if that's your thing also. I think it's a great specialty.
Another specialty which is pretty laid back is occupational medicine, which has quite a significant # of jobs. Most of the jobs are in clinics, with regular 8-5 type schedules, seeing a variety of pts. You can also do more corporate type stuff - reviewer, etc. which pays a decent salary without the intensity of many other specialties. Sure you will likely not make a ton, but somewhere around primary care salaries with a lot less stress.
Also not that many US grads go into it, so not hypercompetitive either.
I agree with you that burnout is a big issue, and certainly don't go into a high intensity field if you are burned out.