Well, I basically did this when I moved from the mainland. I fit as much as I could into a pelican case and left everything else behind. The final cut was:
1)AR 15, 5.56, 20" stainless heavy barrel, free floated, custom milled muzzle brake, SWFA scope and ADM mount. Basically a DMR style/overweight hunting gun
2)AR15, 300 blackout, 16" dissipator. Versatile lightweight brush gun in a caliber that I had hoped would be more available, but found out it's not as common here as it was back home.
3) Ruger security six, 357 mag, 6", stainless. Tough as nails workhorse pistol, double duty as a hunting gun, and fully compliant with HI's capacity limits.
4-5) I cheated and brought 2 H&R hand rifle frames with 5 barrels in 300 blackout, 410/45 colt, 243, 22 hornet, and 2 different choked 12 gauge barrels.
If I'd have known what I know now I'd have left my AR15 in 300 blackout back home and took my Remington model 8 in 35 Remington with its professionaly mounted antique Lyman scope. If I'm gonna have a gun I can't find ammo for it should at least be a pretty gun... But really I'd have swapped it for my Savage mkII 22 bolt action. There's more 22 on shelves here than I've seen back home in years!
Dream list is a phased plasma rifle in the 40 watt range, blunderbuss, nerf vulcan chaingun, M41-A pulse rifle, and a potato gun with a large supply of "personal massager" ammo