I am not certain the HD2 or 3 signal can be considered the originator.
I think the FCC rules say "feed"....which is a method of getting it from here to there.
Let me try again to clarify:
A translator that's licensed to rebroadcast an FM station may legally (under current FCC policy) rebroadcast any portion of that FM station's programming. It can be the main analog/HD1, or an HD subchannel. This is not codified anywhere in Part 73 or 74; it's policy based on what Audio Division staff have allowed.
The FCC licensing process looks at what the originating station is and how its signal does (or doesn't) encompass the translator's signal. If the translator's signal is entirely within the 60 dBu contour of the originating station, it's a "fill-in" and the "feed" can be anything the licensee wants to use - direct OTA pickup, microwave, internet, telco line, whatever. All translators of AM stations are considered "fill-in" translators and can be fed by any method.
As noted above, there are separate and much more strict rules for non-fill-in translators that extend the reach of a primary station. For commercial stations, those must be fed off the air. In theory, I suppose you could use an HD subchannel's programming if you were able to pick up the HD at the translator site, but I know of no such case in actual practice right now. And as noted, the other restrictions on non-fill-in translators include a separation of ownership and much lower power levels.
As for AMs? No AM station has been allowed to shut down and originate programming on its linked FM translator. Several AMs have waited out the four years after the 250-mile window, then moved the AM programming to a sister FM's HD subchannel to feed the translator and then shut down the AM. In those cases, the new parent station for the translator is considered to be the FM station. It's still not originating programming itself.

