The class system came about to describe a very obviously tiered class system (cf. The Two Ronnies).
These days, I wouldn’t go as far as to say we live in a classless society, but I don’t believe that the traditional three-tier system really applies any more (because if it did, you wouldn’t have to ask the question). So you’re trying to fit a society with many levels into a definition which only holds three, meaning that your ‘edge cases’ are suddenly the majority.
Arguably, I’m middle class. I work in IT, drive a Mondeo, and have hobbies including mountain biking and rock climbing. But I only need to drive round, say, Harrogate or Waddington, to get a painful reminder of what middle class looks like, and I’m not it.
Arguably? You’re middle class.
What you’re not considering is the extra dimension. The tosser dimension.