I just bought an R34 GTR through a Japanese dealer. Let me know if you want more information.
Your plan of putting only 50% down on the purchase is, however, unlikely to succeed. Even if you get some mate at customs to do some dirty work for you, the Japanese dealer is unlikely to want anything to do with it. It's money upfront all by the book.
Before you say anything, I did already try this. I didnt even ask about reducing it by 50%, I suggested a couple of thousand - just to the point where i wasnt paying any LCT. But alas that was considered impossible.
Also I think you're being slightly optimistic in your price expectations. Expect to pay at LEAST 50k for the car in Japan FOB price. Then factor in shipping and the taxes, customs, LCT, compliance, rego, comprehensive insurance, good alarm since your insurance company will require one and the car probably wont have one... etc etc.. You're looking at very little change from $75 - 80k on road. Even at mates rates.
If you want some more info, pm me.
If you buy a cheap GTR in Japan, i guess you end up with exactly what you paid for...