If I'm reading this info correctly, & I hope I most certainly am!
I'd first try a 8x57JS headspace gauge, if that works with the go gauge & provided that the head diameter isn't too large (try a line of thin sticky tape around a case & see if that goes in easily or not), if it doesn't then then you should be able to fire them.

I guess if it falls in then you may need your chamber reamed with the 8x60mm, or take a turn or two off the barrel & rechamber to 8x57JS?
Best done with the gunsmith this one.