The ZX n/a 81-83 is the 'close ratio' 5 speed. I don't know why, because the 1980 5spd has a shorter 5th gear. The 1979 box has a shorter 1st>2nd which makes 2nd>3rd shift drop quite large. I currently have the 79 box on my L20b, and I'm going to put in a CR 83 box.
According to sources online, the 240z 4 speed has these ratios 1st 3.549, 2nd 2.197, 3rd 1.42/, 4th1.00 These are extremely wide gears, but would work with a low geared rear end(3.54-3.70) for decent street driving.
The 'CR' box has the following ratios 1st 3.062, 2nd 1.858, 3rd 1.308, 4th 1.00, 5th 0.745 which is good for use with a high geared (3.90- 4.6 ) differential.
Dropping in the ZX box will make the first 3 gears much taller and closer to 4th, if you currently have a 3.90 rear end this will be an optimal setup for the track.
This will completely fix your problem, 4th gear WILL be the same, but you will use 3rd gear for longer, and have a more usable 2nd gear for low speed(45-50mph) corners.
Unfortunately, you will get a ton less acceleration off the line in 1st gear with a low torque L16, and it might feel a bit sluggish until you get to the powerband in 1st, after that you are going to be going a lot faster. This effect will decrease depending on your rear end gearing, a 4.3+ would be very nice for an l16 or even l20b and may make 5th gear usable.
Short story: GET THE CR BOX!!! You will never regret it!