If you scare them away frequently enough, they may learn that large congregations are not welcome. You will always have a few that come by, and those few will not be so messy.
I let our dogs outside for the day, and they enjoy sitting around the pond. They don't chase the birds, but their presence is enough to keep the big flocks away, even though I usually see a few birds at any given time who are daring enough to still come bathe.
You might also look into what types of plants you have around your pond. Something dense like irises limits their ability to easily access the edge of the pond. A ground cover like moneywort holds a lot of moisture, so after it grows over your rocks, the bird waste is dissolved faster and you see a lot less of it. You could also grow grasses/reeds around the rocks which would simply help hide the waste.
As for the waste that ends up in the water, there's probably only a couple of options here. You could add a skimmer in an appropriate location to collect everything floating in the water, or you could add plants in the water in a spot where the waste will naturally flow downstream into the plants. The collected waste will attract certain types of bugs, and between the bugs and the water flow through the plants, the waste will get broken down.
