So I took a good look at the front tires, and I had failed to notice that one has a more aggressive ag tread than the other. Presumably this could at least partially cause the issue. Also, both rear tires are loaded, but one seems nearly 100% full while the other is about 80%. I understand that all of these things could possibly make for steering issues, but I suspect there is still something going on with the power steering system itself. Seems like it may not be worth going nuts over it, at least not until I get front tires that match.
Haven't had time to remove the cylinder, but thanks for the advice, this seems like a simple test and makes sense to me.
I did do this - as you said, easy with the loader on! The wheels don't move from center on their own. However, if I steer all the way to the left (cylinder retracted fully) and let go of the wheel, the front tires will move back towards center a bit, maybe a few inches of steering piston movement. There is no movement if I do the same in the other direction. I did also notice that I can easily steer the wheels to the right just by pushing on the tire (i.e. standing next to the tractor). Much harder to turn the wheels to the left.
Not to hijack my own thread, but I will probably be ignoring this issue for the time being. Once I got the owner's manuals and started going over the tractor more closely, I discovered some really ugly stuff. Turns out the seller lied to me outright about the condition of the machine and went to some effort to disguise serious issue. Pretty quickly, I realized the hour meter wasn't working. Then I saw that the tranny, which I thought was a bit low on oil, was empty. I filled it up, and within a couple of days, oil started coming out of clutch housing. Removed clutch inspection hole cover and a few gallons of tranny oil dumped out. The inspection cover, including the weep hole, was sealed with RTV silicone. Then just yesterday I discovered that the oil pressure sensor was removed and replaced with a plug, wire disconnected and tucked up under dash. I guess an open circuit registers as high oil pressure on the gauge - I sure wish they made it the other way around. I'm off to grab a oil pressure tester - hopefully pressure is OK, and somebody was just too lazy to replace a leaking sensor. But at this point, I expect the worst.
Anyway, clearly some carelessness on my part, but also some outright deceit on the seller's part. Live and learn. For what I paid for it, it will be worth it to fix the tranny leak, but I'm not so sure about low engine oil pressure.
OK, thanks again for your help.