Looking again at the photos you posted, I don't think the exterior has been sand-blasted, but I could be wrong. In particular, the way the pattern continues across the base makes me think that the decoration was applied at the time the piece was made.
As for the maker - well, I'm completely in the dark. I do wish that glassmakers would sign their work! I'd put it rather later than 50s or 60s (which would have ruled out Mdina, anyway - the factory hadn't started then). I wouldn't rule out one of the other Maltese glassmakers - but my knowledge is limited to a single piece of Phoenician glass!
Is there a studio glassmaker in Australia whose work we should be looking out for?