First, I agree--it sounds like there's an issue with your router. What you're looking for would fix it, but it shouldn't be happening in the first place. And I also agree that it's not possible--Macs do their ethernet negotiation through the OS, best I can figure.
Second, I admit I've really wanted to do this myself for a somewhat similar reason; my work G4 is plugged into one of the gigabit ports on our switch (midrange 48-port 3Com), but it takes a REALLY long time to negotiate a connection (maybe 20-30 seconds as opposed to 2-5 for the 100BT ports).
This may or may not be normal (I've never worked with 1000BT before), but the result is every time I put my computer to sleep I have to wait for it to re-initialize the network connection after waking it, and it's annoying.
Interesting that the IBM workstations we have appear to have some sort of self-sufficient ethernet port on them, so they'll negotiate a conection even if the computer is off (the network light on the front blinks even when powered down). I suppose you might be able to get a similar effect by using a 3rd party ethernet card in your G5, but I've never tried that.