In all the years I have been familiar with these Toyota 7F and 8F GCU20s & 25s, I have never encountered a steering issue similar to yours that was anything other than a worn and bypassing steering cylinder. The typical operator complaint that we get (when there is a steering problem) is that the truck wants to drift to the left or right without any input from the steering wheel whenever the truck is doing a long straight run of the dock.
I admit that your description of having to turn the steering wheel 10 full turns to get the steering to react fully is a bit more than I have ever dealt with.
You said the problem was not present when you checked it "cold", that too is a detail to consider. Hot oil will bypass much more than cold oil.
I don't see your reply about whether or not you actually did the test (suggested by snowmonkey) of loosening one of the hoses on the steering cylinder to determine if oil is flowing out of the fitting on the cylinder when the opposite side of the cylinder is pressurized by turning the steering wheel. Note that the cylinder must be positioned so that the steering ram is completely extended on one side of the truck and completely retracted on the opposite side of truck before loosening a hose on the cylinder.
Note which way you turn the steering wheel to move one side of the cylinder to full extension, you will turn the wheel in the same direction after you loosen a hose on the cylinder for the test. The hose you will have to watch for bypassing oil flow out of the cylinder is the hose on the side of cylinder that is EXTENDED. After the hose is loosened from the fitting, start the engine and turn the steering wheel only in the same direction as you turned it to position the cylinder for the test.
If you see any oil run out of the fitting the cylinder is bypassing oil.