Hey OP, a few more thoughts.
1. Proper storage at home is a thing in Mass. as has been already mentioned. Be advised that ammunition and reloading components also required to be properly stored in MA
2. When you are taking your firearms to new residence be aware of a Few land mines in Mass and whatever states you travel through regarding transport of firearms. In Massachusetts transport rules only apply while you or someone is with vehicle. If you leave vehicle unattended then storage rules (not transport) apply
When you travel through NY state (avoid NYC at all costs) NY recently (2 years? Ago) went with similar rules for traveling. Transport rules if with vehicle and storage rules if not. Plus gun cases must be out of sight in NY. As an added feature NY does not recognize FOPA in general except it can be actively used in defense after your arrest. ( this may have changed).
I am not up to date on Connecticut rules
3. What I did moving in and out of Mass was I used a metal job site lock box for tools to transport firearms. Firearms packed in box, box was locked and then transported in a locked box trailer. ( or you could use truck)
As tool box is not a gun case or gun vault it circumvents issue that a locked gun case is considered a gun in plain view and you no longer have 4 th amendment rights that seems to be a new issue
Good luck on move.
PS. In Massachusetts I’ve seen some creativity in what people used as “stealth” gun cases for long guns. Cases for musical instruments. Padded cases for skis or snowboards. Hard or soft sided cases for golf clubs used for checking on airlines. These all useful in getting firearms between apartment and vehicle.
