Here some other ideas:
1. Contact and/or visit some of the classic board shops. A classic board shop is truly a surfer’s store: boards, wet suits, wax, and employees that actually surf. Inquire as to whether they’d sell you a board and store it for you for a nominal fee. My guess to what a nominal fee is one that ranges from $50 to $100 per year. An internet search identified many surf shops in the area, but I’m sure not all of them are classic board shops. Here’s three that appear to be and this is not an endorsement. I left the New Jersey shore far behind in 1978.
https://www.brightonbeachsurfshop.com/https://www.wavehogsurfshop.com/#/http://www.fariassurf.com/2. Variation on #1. Contact one of the more notable surf instruction businesses in the area. Inquire whether they’d sell a board and store for nominal fee. They may offer to rent, but you can explain what you’re trying to possess and store your very own board. Try Surfing with Nicole (of which, I have no affiliation with).
https://www.surfwithnicole.com/