Fuel sending unit issues are a known problem with early C6s
1) See if the dealer will fix it for you.
2) The factory service manual will tell you to drop the tanks… which means droping the rear suspensionand transmission exhaust etc. You want a lift to do this….
3) There is a short cut method involves dropping the tank a little and reaching up above and disconnecting the cross-over lines. Then dropping the tank enough to get the sending unit out. Method 3 is documented in a few places including Youtube.
Couple of hints
a) make sure you get the right sending unit. It has to match the otherone in Ohms (full vs. empty). I would use a scan tool to double check even if the dealer looks it up by your VIN.
b) consider doing both sides (sending unit must match what the computer is looking for…)
c) If you have clutch or transmission issues, now is the time to tackle that as well. Headers and exhaust can also be addressed.
d) Look for a local corvette shop and talk to them about it. They won’t charge you the full dealer bullshit price.