Tractor Help! Screwed up, need advice

Ok so I made a pretty big mistake today on my tractor. Yesterday I had a hydraulic line bust while operating the front loader. Lost a good bit of hydraulic fluid, so I grabbed a can I had under the carport that was still about half full. Topped off the hydraulic fluid level.. Started it up and operated the front loader and backhoe to make sure all was working normally and noticed one end of the new line was leaking hydraulic fluid, so I went to tighten it and noticed the fluid looked very milky white.. Uh oh... I go and pour some of the hydraulic fluid out of the can that I used to refill. #)$!. Somehow, the can got water mixed in! The lid was on tight but water got in it somehow, so I just dumped about 2 gallons of water/hydraulic oil into my tractor. And operated the hydraulics, so I now have this water and oil mixture in all of my hydraulic lines.
How in the world do I go about getting this crap out of the lines? I can't drain it and then operate the hydraulics to clear the lines because the lines cant pressurize with no oil to suck up. And as anyone with a tractor knows, hydraulic fluid isn't exactly cheap. So draining it, then filling it back up with good oil and operating the hydraulics, then draining again and refilling until it runs clear is going to get expensive. Does anyone have a trick or any advice on a cheaper way to flush these lines?? Any advice would be greatly appreciated!

Heavy Equipment mechanic is what I do for a living , I have seen this same senerio many times before , what I would do if I were you would be to drain the tank ,and open as many hoses that are easily accessable and get out as much oil as possible , your tank is probally the same as the transmission housing on most farm style tractors , refill it with fresh oil and run it , what is left in the hoses, cylinders and valves will circulate and mix together and there will still be some water in the system , heat from running the machine will eventually evapoarte it out of there , if your not happy with it you can flush it out again , but it won't hurt your machine -----------there are hydraulic filters designed to remove water from the oil , but they are expensive , it will probally take more than one to do it and the amount of water that they can handle is not much and you throw them away after one time , Reliable Industries in Elmwood is a source for hydraulic oil water seperation filters , another problem is that they don't have all styles of filters in these water seperators and the one on your machine may not be available , in these cases another filter head can be plumbed into the system , but that will run up the cost also , and it would just be cheaper to dump and refill a couple of times -----------you are probally using tractor fluid which is also called HG fluid which does cost more , you could fill it with cheaper R+O hydraulic oil and run it thru the functions for a while then drain it and refill with the proper oil , the mixing of the two oil won't hurt it

Thanks for your response. Your method makes sense. I will definitely try what you suggested. Thanks a lot!