Hamptons homeowners hoping to cash in on deep-pocketed golf fans during next month’s US Open are discovering that $100,000-a-week rental dreams may have overshot. Rental prices across the ritzy beach enclave are slipping ahead of the June 18-21 tournament at Shinnecock Hills Golf Club as inventory piles up and demand falls short of expectations, as Bloomberg News first reported . Average nightly rates during the championship rounds are down 2.5% from the same period last year to $1,106, according to data from vacation rental analytics firm AirDNA cited by Bloomberg. Available listings are up 17.5% year over year. Shinnecock Hills Golf Club in Southampton, NY, where the US Open is scheduled to return next month, is expected to draw golf fans — though soaring Hamptons rental prices have started to soften ahead of the tournament. Getty Images “The problem is very simple.…