I have a small gas burner weed kille. IT is not by any imagination, a flame thrower. It has a small focussed flame a couple of inches across, which is very fierce when the gas container ( small aerosol sized can) is full but weakens as it runs out.
It is very effective for above ground weeds, but no good for the ones with rambling roots underground. I have a similar problem with japanese anenome.
Rather than cardboard over the area I woud use heavy duty black polythene, well pegged down round the edge, so that the sprouting euphorbia does not lift the polythene and let light in.