I've had 18, yes 18 successful BRGs done out of 20 attempts. The last 8 were done through filling out the claim form and corresponding with the Price Match Team with screenshots as proof. Is this a non-refundable reservation? If that's not the case, what's the harm in making the reservation with the Hilton and then doing the online claim form?
If they are still rejecting you, then you can always cancel your Hilton reservation.
FYI, when I do BRGs over the phone, I always call the Diamond Desk. I find the regular Hilton Honors CS reps to be mostly incompetent when processing these claims.