Yikes. This all sounds really painful for many reasons, not the least of which being that the ModelBuilder to Python exporter is quite flawed. I hope you commit the .tbx as well since if you actually need to revert back to a working model that's going to be the only option that is actually guaranteed to work.
It may be easier to bite the bullet and just move everything over to Python properly.
As far as I can tell there is no API method exposed to export a model to Python, but if you really wanted to you could probably automate the UI with macro software like AutoHotkey.
Alternatively, if you don't care about the exported model actually being executable and only informational, you might be able to use ArcObjects to do something with the IMdModel and related interfaces, e.g. dump all elements and processes to a text file.
Is there really any benefit to what you're currently doing though?