No Chuck, it won't work!
I understand what you are tried to tell me, but when a packet reaches a router which is configured for doing natting, the router treats the source address and broadcast address differently. The router simple hates the broadcast address. The only thing it can do is to take the broadcast traffic and send it to one specific host on the other side. Now if you put 1000 helper address on the interface, it may work, the router will take the broadcast message and send it to all the hosts on the other side as unicast message. Other than that there is no other way to do it through as you are thinking (NAT).
Cheers,
Rajesh