I've heard of them, but never seen a flexible circuit board. The components ON the board will not be flexible.Would all of you agree that the end goal is a relatively simple circuit that can be silk-screened onto a flexible membrane so that there isn't a hard board in the purse?
But anyway the required circuit could be made quite small - much smaller than the inverter, which cannot be shrunk much. Maybe you could just "graft" it onto the inverter? It might even fit inside the plastic shell of the inverter if you were to cut it open.
I do want to reiterate that EL panels require potentially lethal power supply. Be sure to design for a low risk of the person contacting any live component.