Hey Dave,
You want to try to determine whether that water is fresh, or seawater... No real pleasant way that I'm aware of to do that, of course - a fingertip taste test is generally the only way to go (grin)... Your tanks are integral to the hull if memory serves, correct? But chances are Steve is right, I'd guess water is coming in somewhere at deck level. Have you checked the fuel vents, as well? Could water be getting in through those? Diesel is more porous than water, so the likelihood that there is a leak in the bilge, it would seem more likely you'd be seeing diesel in the bilge, as opposed to bilgewater in the tanks...
As we discussed in Annapolis, however, I think what you really need to do for the time being is to install an auxiliary/day tank to ensure you have a clean supply of fuel for each day's run... Deal with the main tanks themselves when you get to where you want to stay for awhile, and have easier access to materials and cheaper labor rates than you've been seeing so far...
At this point, I'd say your best bet is likely to be to go for a full replacement of the old tanks, perhaps with something of considerably less capacity, for the time being... Remember, you certainly don't need large fuel capacity for running down the ICW, you can live with a modest amount of fuel aboard for the time being, seems to me...
Good luck, and best regards...
Jon