The owner told me it was mid 80's and all Shimano 600.
Well, it's not
all 600: the brake levers are Exage, which were below 105. The rear derailleur also doesn't match the front derailleur, crankset and shifters, which appear to be the painted Tri-Color 600 stuff. The rear may be older, or some other model. Also, the brake calipers are much older than the Tri-Color 600 equipment.
Sorry, not much help on the frame. The Italian built frames usually command a higher price than the Japanese built frames, so look for a 'Made in ...' decal. However, any Celeste Bianchi usually commands prices that are irrational.