That setup of your mast hinge is not stock for the SLI Day Sailers. I actually thought the SLI built boats had a standard hinged mast, with the hinge bolted to the deck and a short strut or mast section below deck to connect to the step inside the cuddy, but maybe they offered the one-piece mast as original to the O'DAY built boats on their "racing" version of the boat. Your setup appears to be an attempt to copy the "Masttendr" setup on the Compac brand catboats, and is not a standard DS I setup.
As to the DS II ,the DS II had the one piece mast (stepped through the cuddy top) as standard until around the 1981 model year, with the hinge as shown below as an option. Starting with the 1981 or 82 models (I'll have to check my research) the hinge became standard although the mast still was 2-piece (ie: through deck like the one-piece). For the 1984 model year the hinge was bolted to the deck with no opening in hte cuddy top (see pic below of DS_tabernacle), I think they used a piece of mast below deck to support the hinge, but the mast did not actually penatrate the cuddy top. This continued to be the standard as O'DAY transitioned to the DS III during the 1985 model year and was standard on that model until production stopped in 1989 when O'DAY went bankrupt. PEARSON Yachts-Small boat division became the builder in 1990 and I think built a few more DS IIIs before that company became SLI (SUNFISH-LASER) and they utinmately switched to the DS IV (aka: SLI DS I, now built by CCSB).
My 1979 DS II still has the original one-piece mast, I may eventually add a hinge as it makes stepping/unstepping the mast a lot easier.