I know I tend to collapse my middle a bit and that is usually the cause of the scratchiness but today I really felt the crossovers were working well, I was holding my core strong (at least I think I was) and sitting low over my skate and miraculously holding my outside edge before crossing over but as soon as I'd done the crossover my left foot was still scratchy (I'm going CCW). I'm getting very frustrated.
It's always difficult to say from a written explanation
Sounds as if you might be 'falling' onto the left foot. Could also be that your upper body is turned in too much - you need your weight more to the outside and less twist. Maybe you're just not very confident on that back inside edge.
I'm sure you'll gets lots of other advice, but just try holding the left inside edge after the crossover whilst keeping your right leg in position (off the ice is ok) to get a clean edge

It's not that easy to hold and keep the curve, but gives you some time to work out where your body should be.