Any of the above proposed solutions are quite effective and simple. Anyone with half a brain could come up with such solutions. And yet, why hasn't OP's institution arrived at any of these solutions, and would likely resist such solutions? Quite simply, OP's institution is dysfunctional.
With all things institutional, it's the power and the money that effects real change. While we do bring in money for The Man, it's not on the level of ortho, cards, etc. It's not institution-changing money. Ortho bro or cards wants new equipment to make their work flow better? Done. Psych wants to replace that workstation chair that smells funny and has weird stains? Keep waiting.
At the end of the day, the reality is no one cares about our opinion on how things should be done in psychiatry. Hospitals, admin, social workers, therapists, government, insurance, patients and public all highly value their opinion over ours (i.e., see the thread about no seclusion rooms). But none of these people have, or dare have, an opinion on which sutures or staples ortho bro should use.
It also takes two to tango in a dysfunctional relationship. While people have gotten divorced over less, OP will likely continue to throw up obstacles and provide resistance to getting out of this dysfunction, even though a better job is across the street.