First a few thoughts about backscatter: you should differentiate between real DSN (delivery status notifications) and backscatter (where there was no original email from you to reply to). You should not fight against DSN since it's integral part of the email system, and - despite what some people say - useful most of the time.
Stopping fake bounces to emails you've never sent is not hard, and probably BATV is the most logical way to go. You must be aware of the restrictions though: you have to use your specific BATV mail relay for both inbound and outbound mail, since it is imperative that all your outbound get its keyed sender and all your inbound gets verified. If you neglect this you may get your email bounced by Sender Address Verifying (SAV) servers, or the replies to you may get bounced back by your inbound server.
Using DKIM and SPF may also help to prevent the bounces with less efficiency since it require the recipient to check the signature, but in case you're using a central relay you may implement that easily as well (and for a bonus you make it harder your mail to get spoofed).
As for reporting bounces I see no real benefit in that, even less than reporting spam individually. Most bounces contain little to no original headers, so you cannot report on the original spammer, and these mailservers have often not so professional admins with default configurations and in my experience litte room to change. The time you'd spend on reporting would be mostly wasted.