The O'DAY-built DS I had some form of metal (steel, I think?) reinforcement under the side decks, but Day Sailer Class rules require that the wood coamings be retained. Now, the "good news", DSA specs allow those coamings to be cut down flush with the side deck edge to allow more comfortable sitting on hte side decks, in racing it is common to actually "hike out", that is sit on hte side deck and lean out to windward to help keep the boat upright (most racing Day Sailers have "hiking straps" in hte cockpit, running from just forward of the CB trunk to the aft end of the cockit, you hook your feet under those to help avoid falling over backwards into the water while hiking.)
So, I would check to see what the previous owner used to back up those padded cockpit sides, perhaps, if he/she used wood it has rotted out from water trapped by the padding? I think Spindrift used teak wood for those coamings, O'Day used either mahogany or teak (I think teak was extra-cost option) which are both good boat-building woods and mostly resistant to rot.
Check out the Day Sailer Class Association web site for ideas.
www.daysailer.org
Now, you asked whether the boat is generally sailed while sitting on the seats or the side deck? In most conditions it works out well sitting on the seats. however..... as the wind strengthens, I find that the boat gains stability and can handle the wind better if I sit on the side deck while sailing. I use a tiller extension (AKA: Hiking stick) to help me reach the tiller while sitting there. Just a word about sailing in windy areas, ALWAYS, no matter what the wind conditions, keep the mainsheet held in your hand while sailing, use the supplied camcleat to hold the tension, but ALWAYS keep the sheet in hand, since that will allow you to quickly release the mainsheet in a puff and thus spill the wind preventing a capsize if released just as the boat starts to tip. Also, if the wind is blowing a bit strong, it is best to sail without the jib. and raise the CB a bit to better balance the steering (center of sail area moves aft when only mainsail is used so you need to move the center of the CB aft to balance.
I've included a few pic of Precision/Spindrift Day Sailers, to give an idea of the original set up on those boats. As well as a few pics of O'DAY boats. I see that the side decks on the Spindrift boats are semi-supported by backrests from the seats, more like the original (1958-60) O'DAY DS I, than hte later O'DAY DS I (1961?-1970's) which had very little deck support other than hte wooden coamings. It looks like Spindrift used a fairly narrow strip of teak to trim the edge of the deck so there most likely were never the higher coamings like most O'DAY DS I boats have. Now I'm a bit concerned as to why your side decks flex as much as it sounds like they do.
Anyway, I'd still suggest checking out the DSA web site for some ideas, they have a good forum for questions and I am pretty sure yo uwil lfind several owners of Spindrift boats willing to answer any and all questions.