I picked up a small tube of the PTFE Plumbers Paste and filled the open-wedged piece with it. I also applied a little to the threads, as recommended above, and it went much smoother. The paste on the threads made the nut tighten up much much easier than it previously did and the liberal amount of paste I put in the wedge filled the void where it was leaking. I ran hot water through the drain for about 10 minutes and not a single leak!
Thank you so much for the replies! I've been a member here for several years but it was actually a google search that brought me to this thread. Hopefully future searchers will benefit from the newly added replies.
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