It looks like Python3.7 is in the repo (I can see it with apt-file search python3.7). But my main question is: Will it break anything?
From what I've read, it looks like the best option is to install "pyenv", but I don't know how complex that is or what it will entail.
Note that the underlying problem here is that I have an application in Python that now says that 3.6 is deprecated and it will need 3.7 or later in the future.
I've tried building Python from source (from python.org or whatever their main site is), but that hasn't worked. It builds OK, but then when I run my app, it says something or other isn't found. The problem seems to be that when Python is built (i.e., ./configure-d), it checks to see if certain things are already installed on your system (e.g., the various bits of "SSL" stuff) and if they aren't it just goes ahead and builds w/o telling you that stuff is missing. It's be better if it stopped and told you "You need to install such-and-such, then re-run ./configure")