If you could fashion some kind of cap for your feeders or maybe even use a different kind of feeder? If you put your feeders in the coop, I would assume the gopher would find it's way into your coop anytime the pop door is open. 
I've never had to deal with a gopher. We have them here, but they are few & far between. Never had any problems with them.
	
		
			
		
		
	
				
			I've never had to deal with a gopher. We have them here, but they are few & far between. Never had any problems with them.
	
 
(the yellow wrapper one).  You roll a stick into a ball & send it down the hole.  Supposedly they eat the gum & get "clogged" up 
  
 Every time I saw a mound/hole, I'd roll a stick of gum down and I did buy several packs of gum.  The gophers disappeared, no clue if it was the gum or what but the mounds/holes disappeared ... I never blocked the hole & it's easier to roll the gum after warming in your hand.  I'd roll a bunch & put in a zip lock during the Summer cause Winter it was harder to roll (yes it does snow in AZ). 
  That's all that mattered to me.