New Corvettes come with 5W-30 Mobile 1 from the factory. There is no "break-in" oil. They run fine on the synthetic from the beginning.
These engines (LS1/LS6) have much tighter manufacturing tolerances and require the lighter 5W-30 synthetic oils. Heavier oils do not lubricate these engines well and can result in engine damage. (Loss of HP and increased temperatures also result when heavier weight oil is used.)
On a 30 year old car, I would continue to use the oil recommended in your user manual. For my 1980 it is 10W-30 (dino). If a heavier weight oil is "required", I think you are just masking engine problems that need to be addressed.
On a rebuilt engine I would also use the original spec oil. Mobile 1 is great oil (I use it in my 2003 Corvette and my 2002 Chevy pick-up) but it is also expensive. The newer cars come with sophisticated computer monitoring that tells you the remaining oil life, this allows you to get your money's worth out of the expensive synthetic oil. Changing Mobile 1 every 3000 miles, would just be a waste of money. Keeping Mobile 1 in the engine longer than 3000 miles, would just be a shot in the dark (unless you have oil samples drawn for analysis).