I had this happen to my tractor with a loader and backhoe, 11 cylinders total. Here's what I would do.
Park your machine with the front wheels elevated so the cylinders can retract all the way when the loader is lowered. Raise the loader all the way and curl the bucket all the way. Shut the machine off and drain the hydraulic reservoir. Lower the bucket by gravity and dump the bucket. Maybe you'll need a lever to help it. Almost all the oil will be out of the cylinders.
Vacuum pumps are routinely used to remove water from refrigeration systems without taking them apart. At a high enough vacuum water boils at room temperature and the vapor is sucked out of the system.
Take the return hose that goes to the tank loose at the valve bank and hook the vacuum pump to the valve bank. Take the suction hose loose at the tank and cap it off.
Tie the handles in one direction and let the pump run for maybe 12 hours, then tie the valves in the other direction for 12 hours. Then leave the valves centered for a few hours to suck the water out of the pump. The last would work if it's an open center system. If it's closed center you'll have to hook the vacuum pump to the line that comes from the hyd pump.
Harbor Freight has inexpensive refrigeration vacuum pumps, don't know if they're any good though. I haven't used the vacuum method, I didn't think of it then. It should work, hydraulic hoses should withstand vacuum without collapsing. Yours are probably double braid and very sturdy. Obviously don't try to put vacuum on the reservoir or it will collapse.
