Well it seems you have a homemade wood bed and wood rails. You want to add a bumper? So anyway, the cross member has nothing to do with the brackets. The frame rail can be BFH'ed or a winch pull or a Porta Power. Both areas can be sledge hammered or pulled into shape with the bed off quite easily. (swing room)
I don't see much problem with mounting brackets as is, but can't tell for sure from your pics. Need many more pics with proper angles. I also don't know where brackets mount. I would use steel channel for a bumper and make my own brackets. Maybe the pics I see in your album are old and you have a steel bed on it now that requires a stock bumper to be complete?

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn