I think people are getting hooked up on why ‘should’ you stop and let a motorist pass but that isn’t the issue here. The issue is that the cyclist won’t use the passing places to allow the OP to pass in his car.
we ride a road section to get to the off road section on our bikes that is narrow and doesn’t have any passing places, we either sprint a bit to get to the open section quicker if a car comes up behind or find a place that isn’t a passing place but with a careful lean of the bike against the bank allows the car to squeeze pass. Sometimes we get a thank you, other times we don’t.
I also do this in town, if a lorry or van is struggling to get past I will pull up onto the pavement and let him pass. We all have places to get to, I choose to do it slower on a bike so that shouldn’t mean that all other traffic should drive at the speed of me. If I am holding other people up then I feel I have a duty to let them pass.
But then, I am the type of person that if I have a full weeks food shopping and the person behind is buying a paper / choc bar / packet of sandwiches I’ll let them go in front on me.