I suspect the rear expansion valve. It might be clogged.
I also suspect the rear heater & cooler motor assembly (the blend door motor).
I will investigate both.
The valve repair and refill are good to do, but that still might not fix your problem. So while you're waiting for parts ...
Have you run the built-in HVAC diagnostics yet? Ignition switch ON, Fan switch OFF, etc.? That might tell you something.
Any progress on looking into those items you mention above?
I think the rear blowing hot might be a good clue. If you have AC turned off, but temp set to cold (this should close the heater control valve at the rear heat exchanger, and the AC compressor clutch should not engage, so AC is not active anywhere), how hot is it back there? Then can you make it hot/cold by adjusting temp with the AC still turned off? If so, that would suggest your rear heater valve, etc. is working fine.
Then set AC off, and set the rear temp back to cold, let it reach steady state. Ambient air blowing out, right? Now turn AC ON, so the compressor clutch engages and the AC is "working." Now does that make the rear air hotter? If that is the case, I will guess the problem is with the rear expansion valve. Basically the compressor compresses the freon, making it very hot, it cools in the condenser, then it is pumped to the rear expansion valve (as well as the front AC system, which sounds like it is fine). At the valve, there is an orifice that should maintain high pressure upstream and allow expansion on the downstream side. This expansion cools the freon and allows the liquid - vapor phase change. So the upstream side of the expansion valve should be hot and the downstream side should be cold.
But if there is a problem in the valve, either a blockage that does not allow much flow, or if the orifice is too big to force the expansion/phase change, there will be little or no cooling. There may actually be HEATING since you're pumping the hot (cooled by the condenser, but still hot) compressed freon through the rear evaporator.
If that's the case, you'll need to fix the rear expansion valve, in addition to the other stuff you're already planning to do. One thing to consider is that, if you do have a valve problem, it will affect your pressure readings (perhaps meaning the single-AC charts are needed, vs. the Dual-AC ones). And if you do need to replace this valve, the whole system will need to be evacuated, etc., so the MasterCool special tool is not so necessary.
Since you found a leaking Schrader valve, you definitely need to replace that and you need to refill the system, so most of what you're already doing is still needed.
In addition to the tests above, if you can access the rear expansion valve, it may be as simple as feeling the upstream and downstream pipes for temperature. Upstream should be hot, downstream should be cold.