I looked into this months ago. You can get a fuel injected, low mileage LS1 and transmission with the chevy ECU for about $5,000. Then you'll need a new driveshaft, engine mounts, transmission mounts, and radiator along with miscellaneous this and thats. That will add another $1,500 to the cost. Total labor time would be about 40 hours.
Or, you could be lazy and have someone else do the whole thing for you for about $10,000.
You're right about performance. Same HP and torque as a stock 'vette but about 700 lbs lighter. The V-8 is even lighter than the stock L28 so your handling will actually improve. Now all you need is a budget for new rear tires!