Another thing I noticed after visiting the museum website is that they boast that their chicken coop is over 100 years old! This is amazing, however certainly presents challenges when it comes to upkeep and repair. Additionally, preserved historic buildings must abide by strict regulations when it comes to any sort of renovations, remodels, restorations, etc.
I think this is hitting the nail on the head when it comes to repair of the coop. You are likely never going to effect change in that direction. Likewise, the chicken wire is historically more accurate, so it's very unlikely that any real way to keep the rats out will ever occur.
That being said, there is no excuse, IMO, for the treatment of the live birds to be managed along "traditional" practices, as it sounds like from what you've posted. The lack of worming and lice control and "euthanize rather than treat" method of managing, may be based more on lack of funds, however, or it could be just lack of concern. Hard to say.
Frankly, short of becoming a board member, it sounds like you personally are not now going to be anything other than that crazy chicken lady, and anything you suggest is more likely to cause them to button down harder, at this point.
As I see it, that leaves the options of call animal control, call vector control to complain about the rats, and/or call your local news channel. Animal control officers often know little about chickens, and the neglect you are discussing, may not be obvious, and even a matter of opinion, so you may not get any real changes from that, but it might possibly jolt someone into revisiting management practices, who knows? Vector control may be able to say that they must do something about the rats, but likely that something will just be covered poison boxes, but again, may cause someone to start thinking. That leaves publicity. How that is written depends entirely on the knowledge, or lack of it, on the part of the person they send to report, or investigate, on the story. They may end up seeing it as just a cute and quaint way to "teach history" and that would just be good publicity for their outdated kind of chicken care.
If it were me, frankly, I'd go ahead and do all of the above, then walk away, realizing you have done what you could, and you can't change the ones who don't want to change. Good luck.