I dunno, since he was arrested for blasphemy and as you said the cross-shape had religious significance already... Plus positional asphyxiation was part of the torture/execution process. As far as budget cuts, I think it would be simple to reuse the crosses multiple times. It only took a few days, then the body was removed and you could nail up another one. You could also save by using reclaimed wood, like the old mast you'd replaced on the Ship of Theseus.