Have you thought going backwards?
Exactly what I was thinking as I read BM's post.
One of the first sports cars I ever drove was a Porsche Boxster S. The steering and gearbox blew me away. I stammered as I tried to fathom how people could call the car "entry level". If I only knew.
Since then, I've had the amazing privilege to drive all sorts of cool cars - mostly Ferraris - and refine my tastes. From 308s, 328s, 355s, 360s, a turbo Esprit, an NSX, 550s and a 575M, a 612, various Mondials, a Testarossa, a Noble, Mini Coopers (yes, Minis!), a modified Z06 and an Elise, the Elise brought me the most joy. The Testarossa, hands down, is the most demanding and amazing of the list above. I drove it a lot, too (then the chick who owned it took me for a ride and showed me how to really
drive it). The Elise, while raw and incredible, is still modern when compared to some cars from the '80s. But, in my opinion, the Elise (or, I imagine, the Exige) is today's truest sports car.
So Babak's suggestion seems the most logical to me. Go backwards. Go back to a time when there were no Manettinos, no ASR, no power steering, no lifeless video game-like shift paddles, no buttery smooth manual gearboxes, no featherweight clutches, no functional air conditioning. Go back to a time when the only navigation you had was a ratty, outdated atlas shoved under the seat and the childhood knowledge that moss only grows on the north side of rocks and trees. Go get a four-valve, carburetted 308, or a widow maker Porsche; an X1/9, an MG Midget, an original Mini, a Fiat 500 - something that demands your attention from the moment you get in until well after you get out.
If the Elise isn't enough, get an Exige. If you still want more power without compromising that real sports car feel, I'd say get a Noble. But I think the Exige is probably the rawest thing you could get (outside of, probably, an Aerial Atom or a Caparo). Keep us posted on what you decide.