You do not need FI to get overheating in an NSX. Some cars are prone to it more than others, and we have been battling this R&D at many tracks for 3 seasons now.
A few items that need to be checked before you move on to the next step.
(1) fill coolant bottle to at least 3/4 full (important)
(2) burp all air out of system several times front and rear. If you do not know how, let us know.
(3) make sure that your coolant bottle cap is TIGHT!
Most of the overheating issues we have found to be a slippery slope. Usually starts with the level in the coolant bottle being around the 1/2 to 2/3 mark, and for some reason the car will begin to gas off at this level, causing air in the system, and fluid loss, which just gets worse and worse each session. I have fixed the issue in many cars by burping all of the air, and running a higher than normal 3/4 level in the tank.
Here are the next steps....
(4)If the fins on the oem radiator are bent (pressure washer, stones, etc) a new radiator may be needed.
(5)add a higher pressure radiator cap try 16, and then 18
(6)wire fans to work with a toggle switch auto/always on for the track
(7)vented hood
(8)flush system and add water wetter per instructions when re-filling
(9)try running a mix that is closer to all water (not tap)
(10)aftermarket oil-cooler (it will actually help coolant temps stay down)
(11) larger radiator
(12) try FAL aftermarket dual fans
(13) top and bottom ducting to force all air in front of radiator to go through it, and not up or down around it.
On my "not tried yet" list
(a) run a lower temp therm.
(b) run with no thermostat
We have one more car to get to the bottom of some overheating issues, and I will be back to work April 9th @ Road America, but with the cool ambient temps, it may not show itself.
Good luck