Up to 600v you can combine circuits of different systems in the same raceway provided they are all insulated for the highest voltage-- 300.3(C).
Since a metal raceway would be allowed as the EGC for the 120v and 277v circuits, and I find no language that prohibits it, a single conductor EGC would be allowable as well. Circuitwise, the pipe and conductor work the same way.
The issue seems to be, if you are coming out of two different panels, which you would be, is it proper or necessary to make a three wire splice of the ECG at the common J-box and run a separate wire from there to each panel. I say yes.
If you had a metal raceway, that's the way it would be too, so I had imagined it the same way you are describing. If you ran separate EGCs for the whole run, you'd still have to bond them to the metal boxes, so they would be bonded together at that common point anyways.
One grounding conductor per conduit sized for the largest circuit within the conduit Doesn't matter if its six different systems in it. Only exeception is isolated grounding. In a ground fault in a properly grounded system the fault will go back to the panel with that supplied the fault. Each service if grounded properly is bonded together for zero potential. So no one becomes a bonding jumper themselves