I'm thinking it's a III, rather than a II, although the two models look a great deal alike.
The biggest differences between them are that the aft freeboard in the III is taller than in the II, and that the DSIII jib sheet cars are mounted on top of the coamings, in molded pockets, rather than on the inner sides as with the DSII.
Your photo of the boat hanging from the crane shows the jib sheet cars on top of the coamings, so that suggests to me that it's a III. Your transom looks a tad higher than mine (1980 DSII) and the bottom corners, while rounded, are a little more squared off (that could be just the way the photo looks, though).
There's a chart of hull identification numbers for the Daysailer range here:
https://daysailer.org/Hull-Indexwhich gives the HIN range for the DSII, but not the III. However, you could assume that if your HIN is not within the listed DS II range, it's a III.
One more thing to check, which may or may not help: My DSII transom is 17-1/2 inches high from top to bottom at the center (the highest point). If yours is taller than that, you've probably got a III.