Graham,
We're going to make a modification to the sine wave generator you've constructed by powering it from a single 12 VDC battery (get the drift here?), amplify its output and then run that output through the rectifying/filtering network you've also constructed: DC to AC to DC.
Now, understand that there are, obviously, way[/B better, more sophisticated and smaller circuits to do this, but we're gonna use what we've already got.
This approach is called "proof of concept" confirmation.
This is going to be fun...
CBB