Version control for research and teaching statements
My research and teaching statement have a lot of commented text (I write in LaTeX). This is because I amend each document specifically for each job application - as you do. 

The detail in which I describe each topic changes depending on what job I am applying for.  I comment out text which is too detailed for the job to which I am applying. However, for other job applications, I might like to have that text put back into my statement, or write new text, to be perhaps commented out in a future application for a different job.

I now have documents with a lot of phrases from which I can "pick and choose", depending on the specific job to which I am applying, and amend appropriately. It isn't really version control, I know, but I find it useful to have a selection of wordings to choose from in one place so that I can compare and contrast things like the level of detail and the tone. This isn't particularly onerous as these documents do not total more than 2 - 3 pages in my case.