Fault in the Starter Circuit

I drive a 1998 Chevy Lumina Sedan 3.1L. Sometimes when starting the car, it will crank and the engine will start but the 5amp fuse to the starter relay will blow at the same time. After this occurs, the car will run fine as it already started but next time I go to start it after shutting it off I will have to replace the fuse for it to start again. This does not happen every time, sometimes it will happen several times in a row and other times it will be just fine for over a week after I replace the fuse with a good one.

So far, I have replaced the theft deterrent relay behind the glove box, and after doing some research I now suspect the Neutral/safety switch located on the transmission as the culprit.

Before I go through the frustration of getting at this switch to replace it (it appears that the master cylinder for the brakes is right in the way and I am guessing it would not be a good idea to temporarily detach that to make more room), I just thought I would ask an expert and see what you think.

Would it be worth replacing the NSS? Also, is it possible that bad/old battery terminals could be causing my problem? Thanks in advance.