I’ve written a fair bit up about this at http://www.opoudjis.net/unicode/… . All secondary research, but it’s secondary research that seems to have been cited at Wikipedia.
Your timeline is right:
- There was a distinct heta letter for /h/, which looked like H, but it was not used in all locations.
- There was an innovation in antiquity (ca 400 BC), whereby Greeks in Southern Italy broke H in half, and used that for /h/: Ͱ
- From there, Greek papyri use one half of H as a diacritic to indicate an H is present, and the other half to indicate they are missing: x҅ x҆ . (I didn’t write down when, but my page says “by the time Greek starts showing up in papyri”, so it would have been around 300 BC—before /h/ stopped being pronounced.
- Those symbols survived long enough to be passed on to Early Cyrillic, and thus Unicode.
- In Greek manuscripts by the 12th century, the diacritics ended up being curved: ἀ ἀ
- Notice that the symbols were used long after the /h/ stopped being pronounced. In fact, accents and breathings started being notated as diacritics, precisely because they were starting to be lost in pronunciation. They were first used to teach proper speech, and after they had completely disappeared, they kept being used because the ancients had used them.