I struggle to get enough organic materials for proper sheet mulching

Whilst I have plenty of cardboard and a few bags of wood chips, I'm struggling to get anything else! By spring I hope to have accumulated some more! I could cardboard it now and spend all winter chucking more stuff on (soon there should be a cube or so of compost ready, and lots of leaves.
I want to use the area for growing annual crops, and I don't want to dig it (due to erosion, and all the green manure seeds that will now be buried there!)
I've got some big sheets of black plastic I could use... but is it best to put it down now or wait until after winter (and the windy part of the year!)
I think I'm overanalysing things :S