I bought a new grip from Botach Tactical to replace the POS that came standard on my AR.
The problem is that the detent spring doesn't stick out far enough from the new grip to give a positive "click" when moving the safety. Is there any way to fix this without tracking down a longer spring? I'm afraid if I shove something down the hole to make the spring stand higher and it's too big then I won't be able to get it out.

You might try Lowes or Ace Hardware for a longer spring.

I had just the oposite problem with my Hogue grip.The detent spring hole was not deep enough and I had to cut the spring off a couple coils to give the approprite tension.
Maybe you got an out of spec grip also.

Measure the depth of the hole in your old grip, and then that of the new one.  Cut a section of a small nail of the right length and put it into the new grip.   Be sure of the length though - if the piece of nail goes in with a lot of friction, you'll probably never get it out.  Put the spring back in and it should stick out the same amount as with the old grip.