Me too. I know. Doesn't change that it sounds plain wrong to me. I guess probably how "dreiviertel X" sounds to you and others. Germany isn't uniform and only a nation state for some short time.

If I try to rationalize it, it is probably that a quarter (to me) is not a distance or difference, but a single thing. So my internal parser expects a Genitiv or another thing after it, not a preposition like 'vor' or 'nach'. 'Zehn Minuten vor/nach X' sounds fine to me, 'eine viertel Stunde vor/nach X' too, but 'viertel vor/nach X' just doesn't.