If you're working with a single size and layout, then an INDT template file (or an IDML, which is smaller, version-independent, and creates an Untitled document just like a template) containing your styles is a fairly easy fix, provided you can restrain yourself from "tweaking" the styles in individual documents.
If your styles are evolving over time, then after saving a document that contains the latest iteration, you can delete all the content and Save As an INDT, overwriting your old version. That won't change existing documents unless you open them and import the styles from your new template, but it will keep things straight going forward.
I'm not a fan of radically changing the application-level defaults unless your copy of InDesign really, truly will be used only to create this kind of document. Loading a set of text styles from a template or another INDD is something that would be simple to script, though. A script can be assigned a shortcut key, or could be made automatic whenever a new document is created.
From the way the question is worded, I think you'll find that keeping iron discipline in how you use styles, so that you don't "end up with slightly different versions" in different documents, will eliminate most of the problem.