I’m in a different country with a different system but in general I’ve been cared for well under a multi-health system (despite having multiple illnesses.)
Things I do:
Organise all appointments to suit me
Coordinate teleconferences between doctors
I have a communication book into which notes from each appointment are placed. Doctors also write notes into the book to each other.
Finally,
if someone has a problem with what med has been ordered etc I expect them to contact the other person then and there and sort it out.
I value my time too much to let people stuff me around.