Seeking Kaiser-like medical group for PPO insurance

I'm looking for a new PCP and ideally hoping to find someone within a larger medical center, where referrals/testing/specialist visits are very well integrated, and, ideally, my PCP can actually make specialist appointments for me in real-time during the appointment. I briefly had Kaiser insurance a while back and loved how seamless it was to see specialists in the same place (but hated the conflict of interest of the organization that pays for my medical care being the same organization that decides what medical care I should receive). I'm specifically looking at the Sutter system, John Muir Health in Berkeley, or Stanford Health Care in Emeryville. I know they can have long wait times to see my provider, but I'm not concerned with long waits so much as having everything in one place with administrative ease. Can anyone who has used any of these provide any feedback on how seamless (or not seamless!) the experience feels, with your PCP and specialists working together (or not)? One example is a PCP being able to schedule a mammogram for me, rather than refer me out to a different center where I need to call them, register as a new patient, and jump through hoops to get something scheduled. Thanks for any recommendations on medical centers and/or PCPs that you love (or recommend staying away from!)