I do share your concern for Fred.
First, as long as his water intake is within normal limits (1.3-2.2.L for the average goat), that isn't a major worry. Still, if the urine is dilute (you can check this with a urine refractometer which can be purchase online at sites like Amazon), then it does raise concerns of kidney dysfunction.
And in that case, we would want to consider weaning him off the non-steroidal anti-inflammatories (which Aspirin is also one just as the Banamine and Bute) as much as possible. So, if he can manage on 3x81mg of Aspirin that is such a low dose that it would be preferable to the other options. Otherwise, we would want to use the antacids we discussed to avoid stomach irritation (from the drugs or any uremic gastritis if the kidneys are compromised). Further to that though, we'd be limited in our treatment options for the kidneys (much of what is available is only for companion species). In this species, we tend to just try to increase fluid intake, supplement with electrolytes, and reduce kidney strain with drugs as we are planning to do.
Overall, if the urine is becoming overly watery, then we do need to tread with care. Any vet (no matter what they treat) should be able to check urine concentration for you or a refractometer is usually quite inexpensive. If the urine is overly dilute or with our suspicions, we'd need to think about reducing to the Aspirin alone if he can manage on that. But if he cannot or he shows deterioration, we'd have to think about letting him go. And if we did have to do so, local farm or equine vets should be willing to help you since it would be in their duty of care to help you prevent poor wee Fred from suffering.
Please take care,