Luke, I think Soundguy had a good idea earlier. He suggested disconnecting the line at the cooler and starting the tractor to see how much fluid comes out. You could do that on both inlet and outlet side and determine if the charge pump is working. Just don't let the engine run for long so the transmission isn't damaged further due to oil starvation. That and removing and cleaning the ball-checkvalve on top of the filter assy is about all you can do before going into disassembly.
BTW: I don't think your neutral valves and relief valves are adjustable (you have one high pressure and one charge pump relief). Those neutral valves are also suspect. I think if they are clean and the springs are not broken, they will function properly. I don't think you will have to keep opening up the transmission to make "adjustments."
The problem is that this kind of troubleshooting and repair is best left to a shop with specialists with special tools. Having a drilled and tapped banjo bolt is just one example of a tool that probably most New Holland service departments have and use on a regular basis. By the time you buy all these special tools and learn the intricacies of doing an overhaul yourself, I think you will wish you had left it to somebody else. If you can find a service manager to discuss the issue, maybe he can make suggestions or agree to work on the transmission for you after you have removed it. Splitting a tractor is not that hard, but you also have to have several rolling jack platforms and it can be a huge task for a first timer. If it were me, I'd do the pressure and clog testing of the cooler and filter ball-check and then leave the rest to experts even if I had to wait until I saved enough $$$ to have the work done. Good luck, no matter what method you choose.
EDIT: What I should have said above is that I don't think your relief valve will NEED adjusting. It has an adjustment screw, but once set, it should remain constant for your tractor. I believe if it is failing, it is probably due to trash/crud build up rather than an adjustment. You have varying pressure inside your transmission as it heats up. The relief valve would always relieve at the same pressure no matter what the temperature of the fluid, so I think it is not the problem.