360 .060 overbore too much ??????

Just wondering what is a safe overbore on a 360 block. Do all the things like what year block, core shift, etc come into play, or is .060 safe on any 360? I have that race block bored .060 but filled to within 1 1/2" to 2" to the top in the water jackets and have corresponding stroker kit to go with it. I'm assuming the race block filled that high won't work for the street. I would love to use the stroker kit for the street. I have an 87 360 (standard bore) for a spare block and also a 72 360 .030 assembled short block. Will either of these work for .060 overbore with no problems??