Welcome to the forum Ashleigh, and a few things I would add to Andrew’s helpful post:
– if we used cardboard / carpet / black plastic starting now?
Using sheet mulches only, with no organic matter on top of the soil, means at least a three months wait before planting, even longer if perennial weeds are abundant…
– if cardboard, should we wait to put the 3-6"s of compost on until we are ready to plant?
If you can source compost, I would put it on now and if, for example, it was 4-6" deep then you can sow/plant straightaway, no need to wait for the pasture to die underneath as veggie roots can grow in the compost to start with.
– do we need to dig if we want to do any autumn planting?
As above, only if not using organic matter on top: if you dig now, you can sow/plant almost straightaway, but the digging is purely for speed, in absence of compost, and does not improve the soil. In fact I think it spoils a lovely structure.
– do we need to dig even if we can wait til spring planting?
Absolutely no need to do this!! As the pasture roots die, they leave the soil with a wonderful structure for new growth of all new plants: think of all the small root channels which become air channels. If you can add some organic matter on top, growth is even better.