Sorry for not catching this sooner.
I would suggest NOT registering anything if you do not plan to be a permanent resident. You are within the law not to do so and to register anything, in my opinion, adds unnecessary documentation and potential problems.
If you carry your handgun(s) legally (not loaded, in an enclosed case/holster, on your way to or from one of the few exceptions listed in the law (such as going to the range)), it is very unlikely your firearms will even get looked at.
If they do look at them, it will be in the context of verifying they are unloaded, and I have also heard of people having the serial numbers run to check for being stolen. Since registration is not mandatory and only a involuntary function of buying a handgun in this state for most of us, many of us with old guns have handguns that are not registered and don't need to be, not being registered isn't something the police will be concerned with.
In 50 years of riding around this wretched state with firearms in various contexts and even being stopped for traffic infractions from time to time, I have never had my firearms inspected, nor have I had anything inspected at any range. When asked if I had any drugs or weapons in the vehicle (standard question), I answered 'no drugs, but unloaded rifle/shotgun/handgun in cases in the back.' and that was always enough.