I do feel that the heads in the tanks should have been a wake up call for Andrea to begin with, though. I wouldn't have bought that trophy explanation from the Guv.
I may be missing something in your train of thought but the Guv never said they were trophies. He told Andrea the he kept the heads to remind him of the dangers on the outside of the walls (paraphrasing). Now i thought that was great writing because much like reality he is feeding his women a half-truth. Trust me I do this all the time, not about my head collection but rather about simple things like why I forgot to take out the trash. IMO opinion the heads are mostly trophies but I am sure there is a root to the story he told Andrea.just conjecture but for the sake of argument:
say he happens to decapitate a significant foe, like the bitter that got penny. he thinks this is the head of the monster that took my daughter it to important to just throw it in the pile of the dead. so he puts in a fish tank. few days pass and he stops to think "damn it is really crazy how I have this head in this fish tank". but deep down he doesn't want to discard it so he convinces himself I need this thing, starring at it makes me stronger. I need to prepare myself for whats waiting for me outside of woodbury. Then it just becomes a slippery slope till eventually it's "shoot yeah, got me a whole squad of gaurdsmen" puttin' that head in the tank.no it is not logical to keep a bunch of decapitated heads but they do live in a rather stressful world. personally I think keeping heads is much more therapeutic than imagining your dead wife is stalking you.
But back to my point, than your girl catches you with all these heads you can say:
1. yeah i just couldn't get rid of that and dive into a story about its acquisition or
2. relay the half-truth/lie you've already told yourself a hundred times about needing them as a reminder of the danger outside.
Just wait till she finds his porn collection, than he will really need to be thinking fast.