Too bad it wasn't a 1971 Casting 360 block. They were cast based on the 4.04 340 casting. You can sometimes take them .100 over without trouble!

As stated, the machinist can tell you. The sonic testing determines cylinder wall thickness. There really is no clear answer on going .060 over safely. I've read some rare instances where casting flaws have occurred, resulting in some abnormally thin spots even in standard bore blocks.
***Another option: If it is just ONE hole that needs work, ask about sleeving the cylinder. A buddy of mine has 2 sleeves in a 340. No problems and he saved a bunch of $$$ as compared to the cost of a replacement date coded 340 block.