Shipping by ro-ro Japan to UK is £3-500, containerisation; double that. I would imagine rates to the US are similar. Prices quoted are free on board; so that includes all costs to get the car on the boat. When it gets to the US, there are usually some fees to release the car from the docks storage area, then there are import taxes.
Registering grey imports in the US is a minefield; a lot of these cars don't have an airbag, so you'll have to figure that out for a start. Then there are emissions, though I expect most of these will be ok on that. Biggest problem is crash-testing. At least two cars will need sacrificing for crash testing. This is irrespective if there is an equivalent US model (eg. AE86 Toyotas). Someone might have done it before (eg Skylines), in which case you can present that data.
Oh, and also, all this work has to be done by an federal-approved import workshop who don't exactly charge bottom rate. I was quoted a conservative $10k to get a Eunos Roadster in, WITHOUT crash testing.
If you can demonstrate the vehicle is a rarity, you can get a limited mileage tag (2000 miles a year?), though I don't know how they check on that. Also, how do they define rare; do M2s fall in that classification? There was also an ultra-rare M2 version of the mazda AZ-1 Kei car.
However, its not just the Japanese cars on this site that are of interest. Lots of interesting rust-free US cars 9they don't use road salt over there, plus don't put on big mileages). Japan is a great source for Minis as well; towards the end, it was the biggest market for Minis, including the UK. All of these will be rust free cars. I also notice, Japanese Minis are also very nicely kitted out.
The Mitsuokas are mostly rebodied 5-10 year old Nissan models. Probably not too good to drive.
Still, some of these cars are nice to look at, and to contemplate. I'm pretty gobsmacked how tidy the older cars look, yet they are clearly not restored.