At higher speeds, you can get to about 1/8,000, but what happens at these higher speeds is that they can become inaccurate, and your exposures will vary. That's why Nikon didn't specify the FE for speeds above 1/1,000.
Out of curiosity, I loaded fresh A76 cells into an FE set to ASA 50 and, with the lens cap on in AUTO, pressed the shutter.
The shutter stayed open for 63 minutes, and then closed at ISO 50. Whoa!
I tried it again set to ASA 400, and the FE stayed open for 3 minutes and then 17 minutes. It will vary by temperature and the amount of light to which the FE was exposed a little while before you started the exposure. Remember, the FE is analog, and it's the leakage currents which are defining the long exposure times.