That is not a term I like either. Mainly because so much of what constitutes image quality is dependent upon more than just the DSLR designation. First there's the photographer. Then there's the quality of the glass, which can vary from craptastic to phenomenal, and then you have the age of the camera which can make a huge difference. There are point and shoots today that can easily outperform older DSLR's. An entry level DSLR with high end glass can produce better image quality than a full frame with entry level glass. And any camera in the hands of a photographer who knows what they're doing can produce better images than the fanciest camera in the hands of someone who doesn't.
I agree with everything you just said. And I'm guilty of using the term "dSLR-quality" as a substitute for APS-C sensor size. (I think more people understand what I'm referring to for dSLR quality).
And unquestionably.. there are new "small sensor" cameras that can easily out perform an older, larger sensor.
Unquestionably, image quality is dependent on the glass, on the skill of the photographer.
And unquestionably, 4/3s cameras can produce top notch photos.
But also unquestionably -- Where all else is equal (the glass, the skill of the photographer, the age of the technology. the age and quality of the processor), a larger sensor produces higher image quality than a small sensor. A full-frame has the potential to out-perform a crop-body, has the potential to out-perform a 4/3s, etc, etc.
OP indicated several different desires --- Stay within a small budget, better quality photos (through better lenses), and get something more compact.
So my point to OP, if getting something more compact was a top priority, then the 4/3s was a great choice. BUT... based on the desire to stay within a tight budget and also invest in lenses... and already owning a great camera body.. Whether it might be wiser to stick with what she has. I wasn't suggesting that her photographs would take a big step backwards if she switched to a 4/3s.... but the switch wouldn't be a step forwards. So with limited funds, and with already owning a great camera body, how much of a priority was downsizing.