If you had a transformer with 2 'outputs', one 0-6v and the other 0-12v (assuming your dc is 12v), you could drive the 12v 'output' as the primary and take the 6v off the other winding, the schem you linked us to could then be used.
Take care with frequency you couldnt go lower than the transformers rating, but you could go up to about double without major issues.
Also note this would produce mains voltages on the transformers 'primary', so be careful and dont do it if your not experienced.
You could also as you mentioned use an audio amp module, maybe a tda 2050 or similar, there are lots on ebay.