727 no 3rd gear

If the 1-2 shift works correctly, it can't be the governor. If the 1-2 shift is at a very high rpm (roadspeed actually), then it could be the wrong gov weight for the rear gear.
If the gov flyweight is AWOL then the upshift would never occur, and worse is the pump would be spewing oil into the tailhouse, and all pressures would be reduced, possibly to the point of slipping stuff.
If the gov is stuck, there's a good chance that the 1-2 still would not occur, but at least it wouldn't be spewing oil,lol.
I offer only that ball #3 is missing. This would prevent the front clutch from energizing,and that would prevent the band from de-energizing. But on two valve bodies? I doubt it,lol. But I got nothing else. This #3 ball is only used in reverse to prevent a small hydraulic pressure loss at the 2-3 shift valve; and then in third, to prevent a total dumping of fluid at the manual valve.
So then the air-pressure test is the go-to.But you say she's OK;SO;

But I noticed in the flow chart that if the shuttle valve was stuck in the rearmost position it would dump the governor pressure and thus no upshifts could occur,at all.And I have no idea how this could occur.SO;

Perhaps the governor pressure just never gets high enough to trip the 2-3 shift valve,as in; insufficient driveshaft rpm, or the line pressure is set too high, or the wrong spring installed on that 2-3 valve. But again,at least one of those, maybe two, would have to be wrong on both VBs. SO;
I guess the governor pressure test is in order. There is a port just under the speed-o gear and forward. You'll probably want to see over 55psi to trip the shift.If it gets to 75psi and still no shift, probably the line pressure is set too high. Or the TV is stuck in full on.

In case you don't know; one of the jobs of throttle pressure is to delay the shift-command coming from the governor. And you the driver can vary the throttle pressure with the gas pedal, and so decide when the trans is to shift. But the throttle pressure is a function of the line-pressure. If you crank up the line-pressure, the TP automatically goes up,too. But the gov. pressure is a function of drive shaft rpm, and the cranked up line pressure does not affect it to nearly the same degree. This is why the the upshift rpms change when thye LP is changed. So,yes, it is possible that when you really crank up the LP, you may get the gov.pressure so far outta whack that the 2-3 shift might be jacked to a very high roadspeed. The solution to that is to increase the gov pressure with a change in the flyweight. This same change must be made when jumping 2 or 3 sizes in rear gear, cuz the pressures get outta sync. The other option is to dial back the line pressure.
So at this point I think a governor pressure test is the thing to do.