PhD without Enrolling in Formal Program
I think this is very unlikely, but it would depend on the educational resources that you have access to. If you have a local university you should talk to them and maybe to one or two faculty members there as well as the department head. I assume that your relocation options are currently limited, so that is where to start. If you have a lot to contribute they may make something possible, but expect it to take a long time. But it will likely require a formal relationship. 

On the other hand, there are places at which the on-site requirements are short term. You might have to spend weekends (or one or two a month, at least) at a university remote from you. Such programs aren't part-time, however. It is just that most of the work, even team work, is done remotely. This might be a better option for you, though the travel costs (time and money) might not be small. They can also be just as intense as a residential program. 

Some of these programs, while they are doctorates, may not be PhD programs, though. They may require the same level of research or not. They may or may not be suitable as the basis of an Academic career. They may be intended as more practical/applications based than theory based. 

An online search might turn up something that interests you. 

However, if you seek a career in Academia in the US, you almost certainly need a doctorate that the NSF recognizes as a Research Doctorate. Anything that isn't may get you a job initially, depending on the market, but you will very possibly run in to trouble when it comes time to apply for tenure.