Having now completed my 4,200+ mile trip (see:
Reporting From the Mother Road! ) I can say with some authority that you can certainly take your Z.
I did find that space can be a premium when packing enough cloths and other goods for a trip that long but I managed Ok.
I also will say that long stints behind the wheel can be a bit uncomfortable - there are only so many ways/places you can put your legs/feet and/or move around to keep the blood flowing so stopping at least every couple of hours (rest areas, gasoline, etc) is a good idea.
That said, for a two-seat performance sports car, the 370 ain't bad on a long trip and better than most if not every other in this category plus it's a lot of fun!!!