I was kind of in a hurry earlier, but have thought about your problem a litttle more. To start with, here is a link to a thread that will help you understand the fuel flow in an L60 series tractor. It is more complicated than some of the older tractors.
http://www.orangetractortalks.com/forums/showthread.php?t=35336
I said don't run your tractor, but in theory the water separator should remove the water, and the fuel filter should get the dirt out. However the dirty fuel on its way through the lines can contaminate the lines themselves, a fuel reservoir, and a fuel cooler before reaching the fuel filter. Dirt or dust and water are breeding grounds for "algae" since fungal or bacterial spores could have blown in while the cap was off. This would lead to other problems later. So the sooner you can clean out the tanks the better.
The wsm has the directions for removing the fuel tanks and it is conceptually simple but requires support stands and disconnecting a bunch of stuff. Would be last on my list.
So unless your dealer has some suggestions, I would see what kind of pump or siphon you can rig up and start with the right hand tank.
When it is clean, change the fuel filter and clean out the water separator. Add a biocide to clean fuel.