we have all raised beds 10" deep-we dig a trench as deep as we can,sling in horse poo......little bit of soil,tatey,soil to cover ,then earth up from the mound at the side of the trench-last year we had taters in an area with very shallow soil and covered as best we could with soil available-we were still delighted with the crop(and we eats a lot o' tates!)
so this year should be even better....
got me boiling water at the ready! ;D