Strange handicaps: can anyone relate?

[rei]

So I started playing with EarMaster, and I’ve vowed to make a habit of practicing with it daily. I think I’m severely lacking in some really basic musical facilities. Hopefully EarMaster will help.

I think it'll take a loooooong time, though. I have a rather strange upbringing:
-I’ve been playing violin casually for about 18 years.
-For about 12 years I learned by ear, and only recently learned to read properly.
-I nearly failed intro music theory. Twice.
-I tried to teach myself piano several times; no avail. I’m stuck in melody-land.
-I taught myself moving-do solfege in my head last year with surprising success; I can now solfege in my head fast enough to keep up with mostly anything.
-I try to teach myself to teach myself to think in A-G so that I can transcribe music, but that’s proving to be a lot harder.
-When I dictate music, I always have trouble discerning the middle notes of any chord.
-When I recall music to hum or play on violin, I can almost always start on the right key. That makes me think I have perfect pitch.
-When I’m asked to identify a pitch (either out of the blue or in the context of a piece), I can almost never do it. That makes me think I don't have perfect pitch. Or maybe my inability to identify intervals is the real problem.

My current progress after two days with EarMaster:
-For difficult-to-identify intervals, I have to either visualize violin fingering or punch in the answer in the staff -- but I can only do this so long as I’m in the violin’s range.
-I can only identify major and minor chords with confidence.
-Upwards arpeggiated chords are the easiest to identify because I have a base note to solfege against; harmonic chords are significantly harder, and downwards arpeggiated chords are nearly impossible despite being earlier in each set of exercises.
-In identifying augmented and diminished harmonic chords, I tend to think that the bottom note is the 5th scale degree, which completely throws me off.

Has anyone else grown up with this sort of bizarre (lack of) musical education?