I'm in GBS so hopefully this applies to your job role.
The first thing is that your PBC 3 is a negative blip, but it's not a 4, and it's not recurring. It probably won't be held against you, since you've rectified the issue and have shown (2 years) consistency.
The second thing is that for transfers to other facilities, they often look for 2+ and 1 PBCs. 2 might work, but from what I hear it's not really what they're looking for.
The third thing is your SAM is there to help you. Think of them like HR with your best interests in mind.
They want you happy, they want you growing, and they want you to stay at IBM. They have the tools and information to help do that. Use them! When I asked about a new job role I got bombarded with certifications and information as to how to not only do it, but excel in the new role ASAP. Finding that information on my own would have been tough.
So let's address your questions:
a-- Switch to full remote so I can keep my job, and move back closer to family (there are full time remote workers in my org)
Remote jobs exist. As explained below, there's a "Work Remotely" tab in Project Marketplace.
I also find sometimes it just happens that way. I've always found it easier to prove yourself on a project first, then ask for remote work. It's harder to ask for remote work when the manager doesn't know your skills/work ethic.
b-- Move to a new position within IBM
Very easy. Are you familiar with Professional Marketplace? Find a new project that suits your needs and skill sets (and maybe even your growth area if you have some training/Think40 done). Once you get accepted, make sure to communicate between both Project Managers to let you know you're moving (or working part-time instead of full-time on that project) so that they can fill any gaps in their own schedule.
Getting a new project with your current skills isn't too bad. Getting a new project with growth skills, or a job 2 band levels above you, can be a bit trickier, but I know people who have done it.
c-- Move to another IBM location to start fresh.
This one will probably require a 2+, or a project that really needs someone with your skills. You're not going to be able to easily move if you're just going to be on the bench in a new location, but applying for jobs at other sites and making it clear that (paid) relocation is agreeable to you might get you some extra consideration.
There are also "traveling" positions. I know a guy who spent 6 months getting daily per-diem and living out of a hotel, because he wouldn't relocate and his project needed him. Eventually he just relocated, but it was a great deal in the mean time.