When i was testing that file myself (which predated Mass Extinction), big gowen was capable of consistently handling it.
As i recall one of the games "panda" beat me quite badly when he was running his big gowen file. (Earth Dragon, Duel Wielder, Alligator
The alligator and the "pig" are quite brutal to Renally, and shes far the stronger of the two units. With the side benefit of being an answer for Lebeau and Alphonse SS as well. Def removal or skills that allow the use of straight subtraction of hp work quite well.
Break Renally, you can break the file (similar theories work on dalos), the alternative is to consistently remove their recycles (great spirits).
It looses a lot of bite if something gets the focus long enough.
Alternately, coming out strong with mid-high levels of your own, has its uses as well.
Plus there's always the favorite "Burning Spore" for those hard core Refess out there, not to mention a decent AT creature+judgment hammer works nicely to remove the emp. Not to mention exploding spore (with the ability to get it back from the cemetery) is highly effective in its own right. Sooo good to ignore defense and to literally dismember those great spirits. Obviously for Falkow stat changers are also effective (Agi is key), black cat crossing effect as a SS can do wonders, and works for any file, and can be used by any file as well.
Of course Assassin and Invisible Druid SS are quite useful as well, after all if its good enough for him to use them, shouldn't you return the favor?