So, I know that "doktoro" is also an Esperanto word, because I've read about Doktoro Esperanto. Would we use "doktoro" to refer to, say, a doctor of philosophy, while "kuracisto" is reserved for medical doctors?
Yes. "doktoro" is the academic title.
I believe so.
I used "doktoro", but my answer was rejected. I reported that.
Damne Jaĉjo, mi estas kuracisto, ne esperantisto!
Reteleportas min Skotoĉjo
Fidu min, mi estas kuracisto.
Why is "mi kuracistas" not accepted?
Verbs mean "to do the action associated with the root. Kuracisti strikes me as an unusual word, but if it has any meaning, it would be something like "to docotor" or "to do what a doctor does."