We always hired the neighbor to harvest with a green machine with straw walkers if we wanted to leave straw. If you don't want to pay him, trade some harvesting with him acre for acre or barter with some baling or a share of the straw crop. If not an option, follow the tips the other posters suggested.
I can add this. There are directional vanes inside the rotor cage on top. Turn them to the rear position to move the crop through as quick as possible to minimize break up of the straw. You may want to slow the rotor and drop the concave to the point of not threshing all the grain also to minimize break up of the straw.
Harvest when the straw is tough. You may still find the straw difficult to bale as the straw length will be severly shortened. In order to pick it up with the baler, you may have to do all the baling at night with as much dew as possible just to get it to feed and roll a decent bale.