You may be able to get rid of more of the contaminated oil by parking the tractor with the blade up and so it can go down as far as possible (park on a hump or block?) and then with the engine stopped, lower the blade and then drain the resevoir and loosen the lines if you want. The hydraulic system should purge the air quite easily on it's own once you crank it up after refilling as full as possible. Just cycle the cylinders through full strokes several times and then recheck your fluid level and bring it back to the proper level.
Does your tractor have a CAT hydraulic control unit on it? Have you got a new filter? If it's really bad you may want to take the front off the hydraulic unit and wash out any sludge in there instead of possibly having to change the oil again as it cleans up the system. Very common to have a seal on the control shaft that's letting the water get in. I think you can stack a couple in there to help stop it since the shaft is probably pitted or grooved a bit just where the seal rides, or put on a speedy sleeve to cover the worn area.