When done extracting from the bark what do you do with the new wet gooey bark powder mixture?

Until you are done keep it. Keep everything until you are sure you have a good result. Often you can go back if you make a mistake and save a batch.

Yeah I find myself sitting on "spent" extractions for months... if it's an A/B anyway.

I always end up with some based aqueous phase so that goes down the drain and solvents get reused.

As said, keep until you have yielded all your product because if its poor yield you know that probably there is still something in the mimosa.

Once thats finished, down the drain is where it usually goes. Lye is used normally to unblock drains, so....

btw, remember to check the FAQ and use the search function, a lot of the questions one might have are answered around

I guess I've found the easiest way to get rid of the sludge is to just flush it...

I just hope I'm not flushing too much lye at once and rotting my pipes :O