Orange County in general, and especially Newport Beach, I've noticed, are strict about enforcement of, well, everything (parking, dogs, drinking, etc)
Someone else may want to chime in here, but my advice is to pay for the parking in the lot.
CDM is really a nice place to swim. I recall there is a group who swims there Wednesdays at 6 pm or thereabouts.
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I just park on the street above and walk down. The only thing is on the side streets read the signs for streets sweeping. They don't routinely sweep the main road along the bluff.
BTW There is one more nice spot to swim 2mi south of CDM. Cystal Cove State Beach, extreme south end. You can also do a trail run post swim.
http://www.crystalcovestatepark.org/
Train safe & smart
Bob