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If I were you, I'd change the filter every year and the oil every 5000 miles. Synthetic oil won't oxydize or break down like dino oil, so it will stay good for much longer than organic oil. The yearly filter change (before storing for winter) is the best way to keep the engine in good condition. Check oil level every month or so and smell it to see if the odor is changing. If not, keep the oil till you put about 5000 miles on it.
When you do operated the car, make sure the engine gets up to full operating temps and then run it for a few miles more to get rid of any collected moisture in the engine/crankcase. You should install a thermostat of at least 180F. With such short runs, putting in a 195F stat would be the best option, as it will help the engine get warmer, quicker and help boil off any engine moisture.
I change my oil and filter yearly and run my car almost exactly like yours, mileage wise on each run and total mileage yearly. I use Mobil 1 15W-50 and a Mobil 1 truck filter for the V8. Although I agree that the oil could probably go longer but for the $23 for the oil at Walmart and $12 for the filter, I just change it yearly. Since I also have all originals internal on the engine with the L-82 flat tappet cam, I am not willing to risk leaving the oil longer that a 1 year period. Just what I do, not gospel.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.