Collegefour, thank-you for thinking of my efforts, but I'm afraid I can't offer any help. So far, I've only come acroos one other case of a G=serial number and we think it dates to 1985. The only reference I have to a Royale is from 1981, though tere was an Olympic Royale in 1978 and 1979. I'd suggest you investigate the component date codes using the info at http://www.vintage-trek.com/component_dates.htm . I'd be interested in hearing about your findings.

A77impala, thank-you for posting. This corroborates my findings.