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I actually can hit the driveway with the car in first and I need to be slightly on brakes to slow it and then get on gas as soon as the front clears. Minimal front kissing or none. I haven't bogged yet, even with my X 1/9, but can't do it in reverse after I swapped for taller final gears. If it looks like there's no easy solution, I'll probably need to re-grade the base of the driveway, though I'm not sure how it'll have to look--like a long sine wave going up maybe? At the crest at the top, bottoming the center has never been a problem at all because it seems gentle and long enough. Hopefully regrading is way less than $4K and more permanent than adjustable ride height dampers. And I doubt ride height increasing springs/dampers don't exist for the S2000, nor any sports car.
I would be more worried about the top myself. The transition from the incline to the flat at the top could scrap the underside of the car. Going down or backing up it doesn't seem like it will be very fun either.
Looks like the manual doesn't say specifics on inclines or declines. You will either have to run some math or really have a person looking after while you try it out.
I think you may be OK because the width looks to give you the opportunity to go at a bit of an angle. I could measure mine if you tell me how. This is me going up in my Alfa which scrapes in back at the exact point my S2K does, the exhaust tip. I have to go at an angle in both, but I have a dip and what looks to be a steeper driveway?!? It takes practice. Go really slow. The S2K touches the exhaust tip (AP2) but that only happens occasionally and not really that bad. You can't see the scratch unless looking for it and it doesn't hurt anything, I just know it's there.
I test drove an AP2 at 14 degrees. Though that sounds close, 18 degrees corresponds to abrading about an inch of the bottom of the front. I am dubious of whether it was stock height as it had too-wide wheels with supposedly stock tire dimensions, which make them seem awfully thin.
The way I measure is get a long ruler, stick it barely under the front tire sideways (with the least height), and then eyeball the angle at which the front fascia is going to rub, stick in my angle finder in the bottom and measure it. If anyone else can and doesn't have the tools, you can use two rulers--one under the tire, and the other measuring the height at any distance you want along the first. The second ruler needs to be 90 degrees to the ground, not the other ruler. So a 36" ruler would be 0" at the tire and its other end needs to be less than 11". A 48" ruler would need to be less than 14.5". If you have any other lengths, I can do the math!