Plumbing fix day – I did some quick research and found that you can layer pipe thread compound over the top of pipe tape to help prevent against leaks. Went to the plumbing store, and a very helpful worker confirmed this fact and helped me to choose one that is Teflon based, like the tape, that will work with both brass and plastic. He said that brass fittings are notoriously leaky! So I redid all of the leaky joints and ran another water test. Presto! No leaks! I am officially a plumber now (albeit a novice one, and without the plumber’s crack).