If it were me, I would start there with a complete filter/fluid change. After draining the tank, take a small penlight and shine down inside of the tank and see if there is sludge/debris inside of the tank. Look closely at the drained fluid and see if you see any water contamination, metal chips or sludge in the drained fluids. Take a small hook tool, hook the suction line, inside of the reservoir, with the head on it and flip it around to see if you have a contamination buildup on it. I know the Kubota filter/fluid are expensive, but the hydraulic fluid and filters are about the only thing you shouldn't try to find a cheaper alternative on. Just bite the bullet and get the Kubota filters/fluid. I haven't heard of anyone finding a substitute fluid and filter for the hydrostat system that works well.
When you change the filters, cut them open and pull out the pleating. Carefully inspect them to ensure you don't have any large amounts of metal in them. A little bit of break-in material is normal. From the description you are giving on how it acts, it really sounds like something is in the reservoir and is moving and blocking the suction intake head when it is leaned in that direction. Kubota states that the fluid and filters need to be changed after the 50 hour break-in. Has anyone written with marker on the filter canisters, that might indicate what date they were changed or are they the original factory filters that came with the machine when it was new?