I feel like I'm not helping you guys much, because my circumstances may have been unique, but the honest answer is:

Not much negotiation needed. My uni had what I'd call an "old school AI department", grounded in linguistics / semantic web and RDFs / expert systems, that type of research. I was more into statistics, Bayesian inference and vectors. The mutual impact was lukewarm, and completing my thesis remotely not an issue.

Most programs have a year or two of coursework, then it's just research and writing. So if you're ABD ("All But Dissertation") it wouldn't be a big deal if your advisor is on board. You can do committee meetings over videochat.

I was ABD and took a job, and finished my dissertation in the evenings. I basically just had to fly back to school to defend.