Home of record and State of Residence are two different things. And you get to choose where the military moves you upon getting out, it wont automatically be to your listed HOR.
Good gouge; I just (well a year or so ago) changed my state of residence and hashed this out thoroughly with the JAG and PSD first. HOR does not change for officers. Enlisted can change it everytime they reenlist. It is the place from which you are considered to have joined the military. Once per career (for officers, don't know about enlisted) you can get a shipment sent to you from your home of record when you PCS. I used mine to get all my stuff out of my folks' house when I got my own place. Another guy I know is planning to use it to move his fiancee up here when they get married.
By claiming a state other than where you are stationed as your state of residence, you are in effect claiming that this is where you want to go to when you retire. Thus better to pay taxes there than the place you are stationed where you have no interest. Granted, you can go wherever you want when you DO retire or separate. But, as I understood what the JAG told me, claiming residence willy-nilly can have tax ramifications.
In other words, if you choose to continue listing your official residence based off of the apartment you rented for 5 months in A-pool, the state you switched from can call BS and come after you in court for back taxes. Technically. Thus, it is best from a legal standpoint to switch to a state where you either own property or have some history there through family, college affiliations, or other ways to make the case that you do indeed intend on going there when you leave the military. That said, I am not a lawyer. Caveat Emptor.