I was about 6'2" (but I've shrunk a bit as I've gotten older!). When I drove my Europas when I was in college, my height - or the height of the roof - was never a problem but I knew a couple of extra inches of headroom would be nice to have so when I rebuilt my car, I put a "Gurney" bubble in my roof. It does what it's supposed to do but I have some misgivings. Having my head as high as it is hinders my view out of the window.
When I was building my car, I considered lowering the floor a bit. Rather than lower the whole floor, I was thinking of cutting the rear and sides of the seat area, bending it down and glassing a little lower. I discarded that idea because my seat was going to be all the way back and that would have required modifications to the firewall. I didn't know of any lower seats that I would want in my car. This was before the Internet got going so I couldn't easily research other options and I wasn't interested in building my own seat. This was after all going to be a street car, not a race car so it had to look nice. Also, I didn't need to worry about a helmet.
In retrospect, I should have put more thought into lowering the seat. You can probably get an inch or so by modifying the stock seat if you don't need to adjust it. That may be enough if you don't want to wear a helmet, but you would probably be a able to wear a helmet for a short period, for example at an autocross.