If I were to guess, having dealt with only a few of those in the past I'd say its most likely a 75-78 SHS 270 or 271, or posibly an SHT270. The 600 bits may have been added later but the 600 EX line did start around 1978 but I'd think it would have been more likely to have had a Titlist rear derailleur and Tourney brakes back then. The top tow models came with Dura Ace or Crane derailleurs. The cranks say SHS270 no later than 1977 but they were around from about 1975 or so. You will need to get a few date codes off other components to make a better educated guess. I believe that headbadge started in or around 1977 and ran to the early 80's. The 2nd and 3rd from the top of the line models had forged dropouts and chrome tips on both ends.
My gut feeling is that with those cranks, if they are original, its likely an SHS 270 from 1977-78 with the thought that they likely used those cranks for a few model years till they were used up. I've seen those used on bikes as new as 1980, even though they were dated 1976. For the most part though, component dates don't lag more than a year or two behind the model year of the bike.