This is a tricky problem. Water in an oil system will usually make the oil cloudy, milky or white. The gray color as mentioned earlier seems to be indicative of some type of metal fragments in the oil. When you say that the oil looks normal now, is that light yellow, brown, black, blue? In my Exmark I was using their genuine hydro oil and it was green in color. Some hydrostatics were filled with a synthetic motor oil from the factory. It is not a cheap attempt at a fix, nor would having to replace both drives in your mower, but you might want to change the oil and filters again, flushing the system by changing, letting run for 30 minutes with the parking brake on, and then changing again. This will allow the fresh oil to get up to temp and pull any contaminants through the filters and catch them. Then another set of filters and oil will get you back up and running.
None of this will matter if there has been in fact some damage to the drives. Since I suspect that this system utilizes separate pump/motors with one single, shared oil reservoir, then the easiest and cheapest option at this time is to work with the fluid and filters. Check for leaks in the entire system as well, since there will be some hoses and clamps from the reservoirs to the drives and back. And as always, ensure that everything that you will be touching or working on is CLEAN!! Inexperienced people accidentally contribute to their problems by introducing contamination to the system when checking or adding oil, or when changing the filters.