I found this company in Lynbrook NY that manufactures burlap and polypropylene bags here is a link to their website
http://www.fibcbulkbag.com/index.htm
This company is in Lynbrook which is a 35-39 minute drive to Oak Beach and about an hour to Manorville. I looked through their inventory and they sell burlap and black polypropylene bags with a tie on the end. To me the bag from the Jones Beach photo that the kneeling officer is examining looks very similar to the black polypropylene bags on Tape Directs website .Also, their is something sticking off to the side on the Jones beach bag which could be a tie, the picture of the black polypropylene bags On Tape Directs website contains a tie at the top of the bag .I know its a long shot but this companies location would be very convenient for a local to purchase bags and then travel the routes from Lynbrook to Gilgo/Oak Beach and Manorville. If you put the companies address into map quest and then get the routes to Gilgo and Oak beach its shows Lynbrook would be a very convenient spot to access these two locations or vice versa. I think the burlap from the GB4 and the possible black propylene bag from Jones beach should be compared to this companies inventory. Its a long shot but still a strong possibility just because of the companies location.