The "Ellen Farrant" path - also known as the Jones Beach path, used to get a twice yearly garbage cleanup by the Massapequa Bike Club. Don't think they ever tackled the BP path, but I think there's an historical reason, as the club might have been instrumental in getting the JB path created way back thus feel an obligation to the JB.
The BP path has actually seen maintenance by the state, in that they've gone in about once per year to smooth over frost heaves and other pavement issues.
But no cleanup of leaves, garbage, etc..... and I suspect the state budget recently has seen less work on the old BP path.
I know that CLIMB has only a passing interest in the pavement, for obvious reasons and already tackles a monumental job of getting volunteers onto the mt. bike trails for clearing and repairs, so doubt they will want to take on the paved BP.
So your fears are well founded and I've zero suggestions except a letter writing effort to the state. I've lots of stamps in my desk.