I think the blueberries will send out root shoots too. So those are an easy way to propagate.
As far as the blackberries, we have them wild in the area, but they are unreliable and just harder to harvest since the best tasting are the ground-running variety, the cat-claw thorned berry bushes are a bit more sour-more seed than pulp..
My parents have actually copied a friend of the family and created a blackberry arbor that they use to harvest blackberries. Its a lot more reliable, and the quality of the berry is great AND no stooping. They are propagated from cuttings and root shoots too. I think I have some pictures if you'd like to see them.
Another local fruit variety you might want to look into is figs (local figs are usually the turkey variety, I think). The severe dry weather has hurt a lot of fruit - bearing plants this year, but there's still some opportunities out there to set up for next year..
Regards,
SC