1So, I ended up removing all python installations, and reinstalling things via Homebrew.
2
3which python ---> /Library/Frameworks/Python.framework/Versions/2.7/bin/python Delete the entire Python.framework directory from /Library/Frameworks.
4which python3 ---> /usr/local/bin/python3 Delete the entire python3 directory.
5I was a bit nervous about the symlinks. I initially renamed the ones that were obviously going to cause me trouble. It turns out that was unnecessary. Instead, just use:
6
7$ brew doctor
8Warning: Broken symlinks were found. Remove them with 'brew prune':
9 /usr/local/bin/python-32
10 /usr/local/bin/python2-32
11 /usr/local/bin/python2.7-32
12 /usr/local/bin/python2_DNU
13 /usr/local/bin/python_DNU
14 /usr/local/bin/pythonw-32
15 /usr/local/bin/pythonw2-32
16 /usr/local/bin/pythonw2.7-32
17So, brew prune (or brew cleanup --prune in newer versions of Homebrew) worked perfectly. It removed all of the above symlinks.
18
19Reinstall python and python3 via homebrew. All done.
20
21At no time did I touch the python installation located within the /System folder.
22
23Oh, and to be clear. The answer to the original question is