Configure Options->TCP->APN to be blank. This will prevent you from using non-BIS data.
Find third party applications that can be configured to route data through BIS (blackberry.net). Examples include Rove MobileSSH and Rove Mobile Desktop (VNC/Remote Desktop client). Unfortunately, I have no idea whether Opera Mini can route over BIS.
Another (more risky) example is MobiShark.com
which has software that allows you to tether over BIS. Yes, tether a laptop to a BlackBerry as a modem, but route data over BIS instead of the regular APN. Don't think the carrier would be happy with unlimited tether data on a pay-as-you-go though!
Mind you, test first with light usage of anything. It's possible that they may still bill for data, if they found a way to filter BIS data on a per-application basis. (Probably via Service Books filtering: Anything that goes over certain service books might potentially be charged)