Can’t speak from experience but I would be looking at a frame only, given the situation.
At 400 quid I would have thought any compete ‘proper’ bike is not going to be light, also not sure how widely xs size would be available in the entry level ranges.
Buying frame only, especially waiting for something second hand, should mean a nicer, lighter frame to hang stuff from. I’d highly recommend putting something in the ‘wanted’ section here, I’ve had really good results, even when asking for something pretty specific.