I think mineral oil would be overkill for 4.4 watts. For starters, you would need fancy sealing to get the wires through. I'm sure there are simpler ways of mating the chip with the heatsink.
(This is probably off-topic, but I've given a lot of though to quiet cooling. For starters, you can buy a passive-cooled HD5770, that's over 100 W without mineral oil. A case fan is needed, but a 12-cm one at 7 V will do without making any discernible sound. Similar fans are found in some aftermarket coolers for HD5870s. Then there are passive-cooled power supplies, at least up to 460 W which powers two 5870s nicely. Plus, obviously, fanless CPUs.)
That said, I agree that GPUs are wasteful, and I appreciate your work with FPGAs. But to me the problem is simply power consumption, because the noise problem has already been solved.