You are correct on Acoustic uprights having none at all. It all depends on your design for the EUB though. Most uprights have thick (1"+) necks with thick fingerboards (1/2"+), and they are very short compared to BG necks, so a truss rod is just not necessary or effective. So, if you are going to build a neck like that for an EUB, you can get away with no trussrod. I'd rather be safe than sorry though. But to answer your, question, I would say yes. the steel rod would work.
By the way I think that bloodwood board is going to look killer. I've never held any in my hands though, Do you think it is hard and dense enough to make a good sounding fingerboard?