OP, this isn't a problem I've struggled with personally (being perfectly sized at 5'7"), but I used to do a LOT of open-cockpit and single-seat car racing where this is a real issue for a LOT of people. This is a solvable problem, if you're willing to do a little work.
Safety/Tech inspectors are (rightfully) rigid about proper helmet clearance below the roof or roll-bar line. I've raced with 6'4" guys who managed to get the requisite helmet clearance in everything from a Miata to a Euroswift or Van Diemen Formula Ford. The difference is that you can't just leave the stock seat alone and hope for the best:
In either case, you need to get the rear of the seating surface as low as possible. Sometimes on a Miata simply removing one of the two layers of foam from the back end of the seat was enough to drop a driver down. Other guys had to either remove a couple of the jump rings on the springs and replace them with longer links, which essentially let the springs "sag" a little bit for the same effect.
If you're long of leg, you may be able to get more aftward seat travel by modifying the mounting brackets to use offset spacers.
If you're long of torso, you may need to actually
raise the front-edge of the seat a little and slide it a bit more forward than you would expect - this gives you more support to drive with a more bended-leg and reclined position which will get the top of your head farther from the windshield and roof. (This assumes you have long-enough arms and/or telescoping steering wheel.)
If those mods aren't going to do it, look into a fully or partially custom replacement seat. Get a lower-profile seat and custom brackets. Unless your rear-end is on the floor and your back is against the rear bulkhead, you can always go lower and farther aft!
My last open-wheel car was a '93 Euroswift built for a teenagers who were working their way up the Formula ladder. To make the "seat" for my middle-aged body, we temporarily lined the roll-cage with cardboard, sat me down directly on the access panel for the fuel cell on top of a "plastic bag", and poured in a high-density two-part foam around me. After some trimming, a cloth cover, and the addition of a 1/2" camping mat, it was a very comfortable solution. Here you can see the foam still squishing up into the bag around the top of my helmet. A lot of the top portion got trimmed away to accommodate the HANS device, but this was literally molded to my body and therefore VERY comfortable.
EDIT: I should note that a 6'1" "kid" was able to drive in this car's sister chassis by using some of the techniques I mentioned. That guy was fast and "skinny" enough that he was running ballast blocks (~30lbs of lead) - they positioned them forward of his rear-end to form a little raised "front edge" of a seat with his knees bent more sharply. IIRC they had to raise his steering wheel up a bit to accommodate, but the net result was that his butt was actually 4-5" farther
forward than mine in the same chassis so that they could get him really reclined.
