Optimize my Nullifiers
Python 3, 558 511 509 bytes



from itertools import*
E=enumerate
L=len
def s(s):
 q=[(x,y)for y,r in E(s)for x,k in E(r)if k==w]
 for i in range(1,L(q)):
  for c in combinations(q,i):
   m=[l*1for l in s]
   for p in c:
    m[p[1]][p[0]]=n
    for y,r in E([list(r) for r in' xxx ,xxxxx,xxnxx,xxxxx, xxx '.split(',')]):
     for x,k in E(r):
      o=(p[0]-x+2,p[1]-y+2)
      if k==d and-1&lt;o[0]&lt;L(m[0])and-1&lt;o[1]&lt;L(m)and m[o[1]][o[0]]==e:
       m[p[1]-y+2][p[0]-x+2]=d
   if e not in ','.join([''.join(r)for r in m]):return(m)
print(s(m))


Try it online!

It's very loopy, but I don't know enough about Python to optimize it further. I did learn some things from ovs's answer, so that was fun.

The input (modified to make it easier to write test cases) expects ' ' or 'e', while the output uses ' ', 'n' for nullifier, and 'x' for a nullified emitter. The function takes the expected input that was described in the question.

I set the e, w, n, and d variables outside because they could be easily replaced with numbers and, if the input and output were modified to use numbers as well, it would print out the same thing. I used letters because they made it more readable while working on it.

Fun question, OP! Creeper World is great and it was a cool inspiration for the question :)

Edit: -47 bytes thanks to Erik the Outgolfer