If you have hubcentric spacers (ones that bolt to the hub then you bolt the wheels to them) check they are all torqued up correctly but if you have universal spacers (these just slip on over the studs) then I would say they are potentially your problem as they are notorious for creating steering shake at high speed.
I would have a go at the other ideas people have put up as well. If your wheels have already been balanced, you/the technician would have seen if the wheel was buckled as it would "shake" on the balancing machine.
Good luck with it.
+1
I moved when I got the Z to a place with a garage as for me, the piece of mind having it locked up each night is priceless. Is there nowhere else you can park it, friends place, garage off the council? Failing that, what about a car cover?
All the T1-R's are the same so no need to worry about that. Reinforced just means it has a stiffer side wall and the extra load tyres are suitable for the larger cars such as A8's. some larger Mercs etc and small vans until you get up to the commercial tyres. It's all about the weight rating needed for each inparticular vehicle but you'll be fine with the T1-R's.
Sounds expensive to me. I believe I have seen people on here paying around the £60-£70 mark or thereabouts. Afraid I can't help you with a place to go though.