Visiting Shelter Island for the first time - where to park?

So visiting Shelter Island for the first time in a few weeks over the weekend. I know they have day parking but it appears the ONLY beach without weekend parking is Crescent which is a must stop for me since I'd like to try the "on the beach" massage thing they have going on there (which is annoying af since the website seems to say weekends are good but their pdf says otherwise and the parking app wont let me select a weekend - and i would've picked something close but whatever...).

With all that said - I wouldn't mind walking over but the place Im staying is like an hour walk away. And I'd like to bring a beach umbrella maybe a cooler etc to the beach so not sure how that would all fit with a bike rental right of the ferry.

So I'm reaching out to the community - any safe parking within a 15 minute waking distance that could be recommended?? TIA