Weighing my options

Which factory 360 had the compression of a 68-71 340?

None of them.

Why would you want to pull stroke out of a 360? Building a comp eliminator engine?

Buy pistons to raise compressi0on on the 360 and run it, no fancy stuff required. With a good tune, mild cam, headers, intake, carb it would be capable of 12.50 or better et's in a good chassis.