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I went to my local dealership to order some parts and they had an 03 Z06 in the show room, so I hoped in. This is my first time sitting in a z06 and my head hit the lump in the back of the cabin, I tried moving the seat around and the best I could do was having my hair brush up against roof (annoying). The back of the hardtop appears to have a bar going across it (perhaps for structual integrity). So that pretty much rules out Z06's for me :(
BTW I am 6'3" and have no problems with c5 coupe and convertibles. I went over and sat in c5 convetible with the top up just top make sure, I fit fine.
I'd try a couple of other cars, including some 01/02's. There are a number of owners over 6'3" that don't have the problem, and if it were an '03 change, I'd think it might have surfaced before now. Maybe not, but usually there's enough room to have a helmet on (intentionally). The headliner does drop down like you described as it nears the rear window on '02's, however, and probably the earlier ones, too, but that's way, way back there...
Having said that, I do remember one Z seat that seemed unusually high when I was shopping. I attributed it to not getting the seat down or forgetting to adjust it. However, it may be a seat padding issue or a seat not lowering fully for some reason.
In any case, there's also more clearance to be gained by removing some of the springs under the seat. That's a trick some of the driving schools use. Don't give up yet.
THis is indeed a change on the '03's, I just got my '03 last week and noticed this new roof thing right away, although it doesn't affect my 6'0 frame. There are a few other changes that I listed under the observations post.