So how does that work when making star shapes, and such? I've noticed that many recipes tell you to press pieces of the dough into the tray (before scoring into wedges), so would the best strategy be to press dough into a star shaped cutter, rather than rolling it out and cutting it?
If you really want to do the cut outs, make some fridge space and have a few trays handy. I'm in QLD where I find it messy to do any pastry type work due to the heat. If you're somewhere cooler, this may not be as important.
Rest your dough before using. It helps the gluten relax or something. Same reason why you don't over knead it and the blender is brilliant for this. Over worked gluten causes the rock cake effect. I would break up the dough into smaller portions, flatten into discs and glad wrap to rest in the fridge.
Work with one piece of dough at a time, and roll out between 2 sheets of Glad bake (I prefer this brand to others because it's thicker but the 'new and improved' isn't as good). It saves mess and also means less flour is needed to stop it sticking which throws out proportions and makes the shortbread dry.
Then place on tray and chill in fridge (covered). Roll out the next bit of dough and so on. Then take a chilled tray and cut out your shapes. I find it easiest to have rolled out the dough to the tray size, cut out and then remove the excess dough rather than handle the shapes themselves. Chill again. Then bake.