You're correct, they are definitely tapeworm segments. Insects are the vector for tapeworm infections in poultry. It's nearly impossible to eliminate insects in the environment, but not all insects are tapeworm infected.
You are also correct that wild birds can be a carrier from eating infected insects, then excreting their contaminated feces onto your property. I've had this happen many years ago when I lived in south Georgia. It was a constant battle and at the time, due to migrating Robins during the Fall. I had about 20 chickens and at least half of them were tapeworm infected.
I caged infected chickens in the garage for treatment and inspected poop each morning under roosts inside the coops each morning before letting the chickens out for the day. That way I could easily see which birds excreted the contaminated poop containing segments. I also had the time to follow them around the yard while they foraged first thing in the mornings inspecting their poop for segments, then I could catch the bird and cage her for treatment. I was an official chicken poop inspector.
It was an ongoing battle but perseverance eventually paid off. Also, we got freezing temps which killed off the vector for the tapeworm eggs which are insects. The soil froze and killed and wiped out the eggs also.
Tapeworm infected birds can cause blood to show up in feces, same with other worms. I know this from experience. It's not coccidiosis in your birds, it's the tapeworms.
I've dealt with lice and mites as well. Just follow the instructions in post #3.
You'll get through all this eventually, I did.
Here's pics of caged tapeworm infected birds in my garage many years ago:
View attachment 3988536View attachment 3988537