First off, I wouldn't fool around with the shape. The body style is one of the greatest things about a GT40,and with modern materials, you can have a car with no bumpers etc and have an impact-absorbing front and rear.
Second; don't fool with the layout- keep it mid-engine, rear-wheel-drive. But change the transmission to a transverse arrangement like the Ferrari 355 has; it gains you some space inside which might translate into better space for taller drivers.
Third: try to put the radiators in the back, alongside the engine out in the wings, which gains space up front. You could then accommodate luggage which would make the car slightly more practical for touring and so on.
Fourth: roll-down windows, or something for better ventilation than the original has.The changes made on some original cars (sliding windows, vent bubbles, etc) are valuable criticisms of the initial design. There isn't enough ventilation, especially with that big greenhouse in front.
Fifth: adjustable seats. (most replicas have this; the old ones did not, except for the Mark 3, I think)
Sixth: if you didn't have all the plumbing running back and forth inside the central tunnel, you could put the fuel supply in there, like Ford did in their concept car. I think this was a good idea from a safety standpoint- having the fuel tanks in the wing sponsons seems risky, although fuel cells make it safer by far. Also, one tank per engine, assuming it holds enough, is less complicated.
Seventh: make the chassis out of aluminum. That is the best compromise, I imagine, between strength, corrosion resistance, light weight, repairability, and stiffness, with costs factored in. Steel weighs too much, and composites cost too much and require exotic repairs if they are broken. You could save some weight by making the body from CF and Kevlar, or using more modern materials than old E-glass, but the cost goes up.
AND; use an all-aluminum engine, clearly the way to go. It would probably be sohc or dohc design, (if you were starting with a [relatively] clean sheet of paper why use old engine technology), and maybe even have forced induction of some kind, although with a car as light as this would be, maybe 1600-1800 lbs plus driver, you might not need that much power. And, modern engine technology includes things like variable valve timing, EFI, etc.
Well, that's my recipe. Now I'm going to stand back and watch the fur fly...