Work with a professor from non-PhD-granting university in the US to earn PhD?
AFAIK, almost every Ph.D. granting universities requires your supervisor to be employed at that university. The only workaround for your situation is to have your desired professors from other universities as your co-supervisor or co-advisor. Please note that this is something to be decided by your supervisor, not by you. Also, you need to convince a professor from another field to accept your not-related application in the first place.