The reason for the soupy quality is that you need to add browns.
It's my guess that you're only putting in food stuffs.
Need to add bedding -- browns-- now and then.

If the bedding in a vermicomposting bin supports fly larva, maggots, it probably is too wet for the worms. Too much moisture in that mix will exclude the air those worms also need to live on.
One reason why, after a heavy rain that saturates the soil, earthworms appear on teh surface is that in that saturated soil they cannot breath.

I usually keep a good bit of bedding, in the form of shredded paper in my red wiggler bins. But the BSFL seem to like the environment without the bedding. I like the way they process the food waste so quickly. I do not mind the soupy quality of the bin. Actually, it gives me more leach to make compost tea out of.

I am more interested in what to do with the BSFL castings. I did some further digging, (sorry for the pun) and read that the castings from the BSFL is not "stable compost" yet, whatever that means.

I do not have any chickens to feed the BSFL to (at least not yet) so I am more concerned about being able to use the black stuff they are producing. I did find a couple of sites that recommended feeding it back through the red wigglers. but its going to take a little redneck ingenuity to devise an deficient mechanism for that to take place.

yes, it is unstable, meaning it is smelly and full of bacteria. the maggots do not care for chopped corn stalks or anything brown, but to feed it to the worms some adjustments are needed. First you do have to add the browns (sawdust would be ideal), second you have to lower the temperature (20F typically), third you would adjust the pH (trial and error).

The BSFL + worms idea has so many enthusiasts because after the worms you do have stable castings (smell like rich earth), and incidentally you would get 20% of the original materials in larvae, and 12% in worms. Who can grow 1 lb of meat out of 3 lbs of spoiled food?