I think when Trump uses the term Universal care, he means we need everyone covered. Affordable plans that most people can afford and a different system for those that can't afford care.
As far as single payer, there may be ways to do that and still keep providers and insurance companies private and competitive. Any time you concentrate the paying power, there is a chance of government abuse.
I owned a health care firm and it was a relief to see the patient was a Medicare or Medicaid patient and not some private insurance company that I didn't know when or if we would get paid. Or what sort of special hoops I'd have to go through in billing.
Bottom line is you've got government healthcare now, and Trump is probably your best bet at getting it repealed. Congress doesn't seem to show much interest in it, so you're going to have to have a cheer leader or a bully pulpit to motivate them.
I appreciate your particular experience, but all the doctors I know feel pretty much the opposite. They are increasingly looking to drop Medicare or Medicaid because the reimbursement is't enough to make it worth their while. In fact, we recently had to move a friend of the family who is getting old because we couldn't find many doctors in her area who would even take the gov't health plans. Ended up taking her to NYC where at least there were more options for people in her situation.