Just remember that you can never get all the water back out of your tires without removing them from the rim. I think your worries about excess weight when mowing is over emphasized with the tire ballasted. As long as it is dry and you dont skid the tires, you should not damage the grass any more with loaded tires than with none loaded. The Pound per square inch loading is not that much more significant compared to the stability and traction advantage that you will get. It is just not practical to put water in tires and remove it. Same with adding weights to the rear wheels. That is not so easy to do that you want to put them on and take them off every time you need to mow.
If your situation is that critical for damage, perhaps your better solution would be to get a small riding lawnmower for your immediate lawn needs and use the tractor for the area that is not so close to your house. Like my house site is, I have a 12 acre lawn but I mow most of it with my bushhog and the acre or two around the house I use my 52" ZTR and/or 48" lawn tractor and push mower and even a weed eater in some of the totally inaccessible areas.