I don't own a car, but do own a bike. At least where I live, I also have the same single route as you to commute to work (there might be lovely alternative cycle lanes where you live).
No bicycle lanes. In fact, passing while completely in the other lane violates the law because the vehicle cannot be greater than 10 feet from the bicyclist due to how narrow the road is. The bicyclist's presence means they are, according to law, deciding the speed all traffic shall flow at. It is odd to me how bicyclists find this to be an acceptable situation and anyone disagreeing to be in the wrong, so much so they will downvote someone expressing direct experience on the matter.
So this is the only road and there's no alternative bike path. It's too narrow for overtaking so presumably there's also not enough space for stopping on the side. You said yourself that cyclists tried to let you overtake which you didn't because it's illegal.
So what I don't understand is what else you think a cyclist can do in this situation other than not existing and bothering you. There's no alternative route.
There is easily enough room for a bicyclist to stop on the side because there are driveways a-plenty plus utility pullouts. These things cannot do anything to increase the usable width of the road for a car.
I see a really consistent trend of people who feel it must be the case that the bicyclist must be justified in what they are doing, then go on to make assumptions that are wrong, just as you here assumed something about the road that is wrong.
Honestly, you could have said from the start you wanted them to pull over.
You started with "Don't ride on narrow back-county roads where you block the regular flow of traffic.". That sounds to me like, don't do it at all, not "please pull over every so often to allow card to pass".