Yes, likely sync on Y. But you don't want to *strip* the sync, you want to do the opposite, to ADD the sync.
You already have the composite sync available to use on the separate pin from the source equipment. You just need a quite simple circuit to impose the H and V sync pulses onto the Y video signal. The circuits I've seen for this have used a single transistor and 3-4 resistors.
No, I think you're nearly done.