How did this work when swapping horses of different fitness? Did people have to negotiate the price differential every time? I can see how it would work for a network like the pony express, but harder to imagine for individuals.

In another article on that blog, the author hints that it was all quite organized:

"William Waterhouse of the Swan with Two Necks Coaching Inn owned 400 horses, which he used to pull stagecoaches for their first part of the journey out of London. By 1817 he claimed to be spending £2 per horse on food, accommodation, tax .Waterhouse had distribution centres all over the Home Counties, including a warehouse in South Mimms in Essex."

https://about1816.wordpress.com/2018/09/12/back-from-obscuri...

"Once they were too old or lame to keep the standard pace they became food."

That is still common in some areas.