The LM could only be flown meaningfully using fly-by-wire, using either PGNS (spelt this way but pronounced "pings") or AGS.
Right (and thanks for the PGNS correction, I wasn't sure about that).
The LM and CSM were both purely fly-by-wire in that every thruster was controlled by solenoid valves that could only be actuated with an electric current. But Apollo fly-by-wire came in two distinct forms: with and without the computer in the path between astronaut and thruster valves.
While direct-control methods existed to couple the RHC and THC to the RCS control logic
Right. By pushing the stick beyond a certain angle the computer was bypassed and the corresponding engine valves were directly actuated. I suspect (but do not actually know) that this was tested on Apollo 9 but never used operationally. Even Armstrong's much-touted "manual" landing was anything but; the computer was very much involved in making the LM react to his stick inputs as though it was a helicopter.
it is unlikely the LM could be flown manually in this way to a stable orbit.
I fully agree -- astronaut bluster notwithstanding. Gene Cernan says that during his Saturn V launch on Apollo 17, he practically 'dared' the IU to fail so he could take over and fly it manually into earth orbit. I'd like to ask him what he would have done had he lost his (IMU and computer-driven) 8-ball at the same time, especially since it was a night launch.
However, with some guesswork, it might be flown to a suborbital trajectory suitable for one of the eccentric CSM rescue procedures. But they would have only an hour or two to devise and effect the intercept.
Wow, I had not known there were
any suborbital rescue options. That would have been even hairier than the Apollo 13 recovery. A lot faster-paced, too.