Wow, that sounds awful...
So maybe it's not even related to other modules, but some... cache problem somewhere? Be it browser or server-side? A Heisenbug.
It remains a complete mystery. I started enabling other modules on my clean install and boom - off it went again. Of course, removing those modules didn’t make any difference so I couldn’t...
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I may have answered my own question with this old tutorial. Thanks again Mustard Seed Media! http://mustardseedmedia.com/podcast/episode42