I usually spread that matter on 2 layers of burlap on top a working bin. The liquid seeped slowly into the bedding below, the worms moved down too. Fluffed it like 2x/day and after several days the wet muck became a managable VC.
BTW, how wet is your "stuff". Flowing wet? When you "pour" it onto the burlap, you could wait until it stop dripping, then put that on top of the working bin to prevent flooding it.
Hope this works for you.

It's not flowing wet, but it is like a thick mud. I was wondering if I could just pour it into an outdoor compost bin, but something tells me that's a bad idea. :(

You could do that if you like and you do not mind "losing" the worms to your compost bin. I don't think anything can go wrong with an outdoor compost bin. It will fix itself except dryness.