Mesa contract section 17 A 3-Furloughed pilots will file their proper addresses with the Director of Operations or his designee at the time of the furlough and will notify the Company of any address changes promtly.
I don't see that you contacted the Director of Operations in your emails. I do see that contacted HR. Being a furloughed pilot myself I can tell you HR doesnt keep any records of being a "current" employee. They list you as a former employee(so you can file and get unemployment benifits) so they wouldn't have "record" to put your current address in (I know it sounds strange but when I went back we had to do a full application with 10 year background check as a newhire) I would contact Mesa ALPA it does say in the contract that you can contact the "Company" and HR is part of the company. If you have records showing that you called or wrote HR or anyone as soon as your address changed then maybe Mesa ALPA will help you (they love a fight with management)