I found Nikon fe-fe2 service manual online and it shows that we have to adjust RV1
I am not specialist who repairs camera but have fun to find solution in any broken thing.
I used small screw drivers and other tools in my house to open the top cover and adjust RV1 (as shown in picture) then cock shutter several times until shutter at 1/500, 1/1000 waken up . You have to readjust - cock - adjust till you get these shutter speeds back to normal. Fortunately that i have a Nikon FM for comparison. Of course, it may not the right speed because it needs special tools to check but i don't have, so i have to test by taking picture , next step.
if you don't want to pay service cost, try this
[sorry for poor English]