I see that the Continental Extreme Contact (weight rating 98, 1653#) is recommended by Tire Rack, but the Pure Contact (weight rating 94, 1477 lb) is rated by several places as quieter and more efficient. The Pure Contact would be good for a total load of 5908 lb, well above the car's GVWR of 5072 lb.
your analysis is accurate - you need a tire that will support the GVWR - thats all.
GVWR is not all you have to look at. GAWR is important as well. Remember that the weight distribution in the vehicle depends on how the passengers are seated and how any cargo is loaded. If you place heavy objects in the trunk along with some passengers in the rear seats, it's quite easy exceed the rear axle GAWR without exceeding the entire vehicle's GVWR.
Using 98W tires with a 1653 lb rating
ensures that you will never exceed the tire's weight rating under any combination of total passengers and cargo, no matter how the weight is distributed, provided that you also don't exceed the GVWR or GAWR. The W speed rating also ensures that this guarantee holds even up to the top speed of the vehicle.
If you use tires with a lower load index, say 94 vice 98, those tires will still carry the vehicle at normal speeds and low loads. However, this opens the possibility that there are passenger and cargo loading combinations that, while they may be within the GVWR and GAWR, may still exceed the tire's weight rating. This is dangerous for the tire and unsafe for the vehicle and passengers. To ensure safety, you would have to do a computed load and weight balance for the vehicle, and also compute a top safe speed, which may be quite a bit less than the top speed of the vehicle.
As most of us to not get out a clipboard and calculator to do a load and weight balance every time we begin a trip in our vehicle, the simpler solution is to use a load index of 98 or higher.
