Yeah we opted for the no dig because we also have clay soil. However we're also working on improving the soil in our yard and were advised to add some gypsum as well as the above suggestions to help break it up - here is some info on that.
Gypsum and Clay Factsheet - Gardening Australia - ABC
Gardening Australia - Fact Sheet: Clay Soil Test

Obsi, have you thought about using the white polystyrene boxes to grow vegies in? Might be a cheap option for you if your greengrocer or something could give them to you?
Gardening Australia - The Self-Sufficient Gardener