"Can we assume that if the main pump is the one doing all the work that it must be working at proper (high) pressure?"

From experience I know it can, and even then it can provide enough pressure to flood the engine should the FPR allow too much pressure to the injectors.
Perhaps the only tell tale of a non functioning in-tank pump is a main pump that starts to become more noisy when the tank is below half or quarter full.

"Can a high pressure pump “partially fail” in a way that it still pumps but at a reduced pressure?"

Yes, I think so. On one trip I felt the engine hold back a little while at the same time I heard a slight howl from the main pump. After filling up the tank, I could drive home just fine. Suffice to say I quickly replaced the main pump.
Later I found the in-tank pump had stopped working due to a sheared wire in the epoxied little bucket on top of the sender unit. The pump itself turned out to be functional.

"So if we assume for the moment that the main pump is working OK then why are the injectors not injecting adequate fuel?"

The assumption that the injectors are the cause is still to be determined. They may actually be functioning properly but an external cause (like incorrect fuel pressure) leads them to inject the wrong amount. Especially during a cold start is it important that this pressure is correct.

The ECU controls injection duration based on sensor inputs. However, during a cold start, it cannot rely on the O2S feedback which - in my experience with a slowly failing FPR - is more than just a "fine tuning" feedback, it actually seems to have a lot of influence.
Without its data, the ECU calculates ball-park injection durations for which it is essential that the fuel pressure is correct.
If the pressure is too low, the mix will never become combustible, the same goes if it is too high.
Gas engines only have a narrow window around the optimum fuel to air ratio in which they will work.

In my case the FPR had failed in a way that fuel pressure was slightly high leading to a good start followed immediately by very rich running (eneven idle, grey pungeant smelling smoke), until a minute later the O2 sensor started giving feedback. From that moment on, the engine ran just fine as the ECU "knew" the mix needed correcting. Hence I concur with those that say fuel pressure should be measured next.

"So are the injectors opening?"

If I'm not mistaken, OP determined they are working by using control function 3.
Note that all injectors are working simultaneously, so if one isn't functioning, it won't become immediately apparent by just hearing them click.
To determine every single injector opens, I would unplug all but one injector and run control function 3. If it clicks, I'd unplug it and plug in the next one and repeat the test until all four injectors are eliminated as a possible cause.

"On the 240s are the injectors constantly fed a + electrical signal and the computer controls a grounding path of varying duration?"

Yes, that is how they are controlled. The ECU "pulls the signal down to ground" when the injectors must open.