There are a number of primary care psych fellowships (also called behavioral health fellowships). None are technically "ACGME accredited," but in the fellowship world many are not to begin with unless you are truly seeking subspecialty certification. When people do those fellowships, more than anything they are seeking training as opposed to the certification.
Now normally, I would go to AMP again for this, but the truth is the links are almost all outdated/broken. For reference, here is the page with fellowship info:
The Association of Medicine and Psychiatry » Fellowships.
Here's what I could find with searching, most are 1-2 years:
University of California - Irvine - Primary Care Psychiatry Fellowship
University of California - Davis - Train New Trainers Primary Care Psychiatry -
Application
Columbia University Psychiatry - Family Medicine Fellowship
University of Alabama - Behavioral Health Fellowship
I'm pretty sure there are more, but its tough to know exactly how many there are. I don't know how competitive these are, but it might be valuable going to the AMP, APA, or AAFP and asking around if its really something you're interested in.
As far as your program is concerned, that's a tough one. If you try to apply to new programs, they need to know, because you'll need a LOR from your PD to apply to another program. That also means having the option to stay and finish is kind of over. I think you need to make the decision to either plan to finish out the 3 yrs in FM, then apply Psych or for a fellowship OR to call this an intern year and expect that you'll be at risk of not being in a residency program after 1 year of training, because that's what you'll have to tell your program.
I'd give it a couple months to think about, but don't take too long, because you'll have to have that convo with your PD sooner rather than later. If we are talking about the most economically sound and safe decision, its better to finish the 3 yrs and then move on, but that's a tough pill to swallow if you have FM and general medicine.
Counseling & Psychotherapy and the day-to-day of a FM doc are very different. I know a lot of people that can't handle/hate the day to day of even outpatient FM. There's no point staying in a medical field that you're miserable in even if you are paid better. Its a disservice to you and your patients, who will be invariably affected by your misery, to do so.