Sorry I did not see this post until this morning, but there are two things you need to check, the seal where the big pipe connects to the pump (on top), and the rubber boot under the right side operator's platform.
I think your pump is cavitating because it is drawing air. I would spray or pour some oil around the inlet to the pump and observe if the cavitation stops or the oil is drawn into the fitting at the pump, indicating the o-ring seal is leaking. If this fitting and the bolts are tight, this is probably not the case.
Under the right side operator's platform, there is a big rubber "T" that is held in place with hose clamps. It's really easy to hit some brush and loosen this fitting or even punch a hole into it. If it is loose or damaged, your hydraulic pump is probably sucking air and cavitating. This "T" is where the oil comes out of the big filter and splits to go to the HST transmission and to the hydraulic pump. Both the HST and Main Pump draw fluid though the big filter between the right rear wheel and transmission case. The fluid then separates at the rubber "T" and goes to the HST and Main Pump. Your HST may be drawing some air too, but it has a charge pump that helps by doing most of the work of drawing fluid from the reservoir and supplying it to the main HST pump. Check the big rubber "T" and make sure the clamps are tight (snug). Don't overtighten the clamps. Like any hose clamp, they will fail if tightened too much.
You said the filter was 1/2 filled. This puzzles me.:confused3: How do you know that? Did you remove the main hydraulic filter? Is it possible that the filter is not seated properly and its gasket is leaking air into the system?
One last thing you should check is to pull the engine dipstick and check the oil level. If the oil level in the engine is way overfilled, there's a chance your main hydraulic pump has blown a seal. This happened to me earlier this year and it has happened to several others. If your engine oil is fine, don't worry about it. This is not your problem.
Please don't worry about disconnecting any quick connects or removing your loader if you need to do that. Your tractor is protected by a high pressure relief valve, but disconnecting the loader quick-connects won't cause any pressure to be felt at the main pump unless you operate the joystick while the loader QCs are disconnected. Even then, it's no big deal.
Please do not start taking apart your hydraulic pump. It is a pretty involved job to remove it and you want to make sure there is something wrong before ever doing that. (This is experience talking. . .

)The main pump and the power steering pump use the same drive gear off the engine, so if something was wrong there, you'd not have any power steering and it would not partially work sometimes. I surely think that you have air leaking into the system somewhere.
I would caution you to not run the engine and main pump for long periods if it is not pumping some fluid. The hydraulic fluid lubricates and cools the pump. If the pump is allowed to run dry for a long period of time, it will overheat and need to be overhauled. You indicated the pump is pumping some and that is probably sufficient to protect the pump, but I would not feel right if I did not caution you a bit.
EDIT: I added some photos. The first is the hydraulic pump and PS pump on the engine. Those two top bolts should be tight and this fitting is the one I'd put a little oil around to see if it gets sucked into the pump because of an air leak. The 2nd photo has the rubber "T" just visible to the left side of th photo. The photo was taken from the left side of the tractor, but the T-boot is large and easy to see.