2003 Chevy Monte Carlo The gas gage is not working properly

When I first start the vehicle the gas gage reads full. It remains on full for about 2-3 minutes then immediately indicates an empty reading. I've filled the tank and driven about 300 miles with this condition so I think the fuel pump and sending unit are probably ok. However every garage including the dealer want to replace the sending unit at a cost of about $700 to $1000 dollars. If the fuel pump were defective I assume the vehicle would not run at all. I wish I could locate just one honest mechanic in my city.