Well… I'd have quite a lot to say, opipik! (even with many images and doc…) but this could reveal my own 2x4 font(s)… [Too quickly, unfortunately. By 'font', I mean a complete basic Ascii design without dupe, yet with tricks and fair-to-bad readability with my personal training.]
I enjoyed:
• your great attempt to provide both cases(!)*;
• your solutions for the squeezed "m", the grayed-bottom "259", …;
• your smallest/simplest lowercase/numerics (no quote on purpose here, because some of them match 'my' choices, but in different grid sizes).
Many interesting glyphs, e.g. italic "ACOU", shrinked "B" top, narrowed "D", inverted(?) "E", cropped "Q" on left, "T" on right (common), "X" without center, coherent "dpla" ;-), etc. (too sensible tips for later about your lowercase, again, sorry.)
Several large (actual 2x4) glyphs look like landmarks in your design ("JQft2579"), which is almost a hack (in a duplicate-crippled pseudo-font, but a working trick all the same, limited to the relatively low occurrence of these characters).

* Of course, I regret you could not get rid of the great deal of doubles (which I will not list, since this 2014-09-28 version is still an early trial - waiting for infinitely more incentive than the download count, knowing that this kind of design/usefulness is quite ahead of its time).
Actually, if you thought in terms of 'bits' (number of cells/blocks), you'd count too few possibilities as 2x3. Therefore, you wouldn't have adopted this layout… *hush* (and you got stuck inevitably from this error with the baseline.)

So, we have a good start if you don't want to achieve basic Ascii. On the other hand, you'll have to enlarge your letters if you want to support the 94 characters of this -old/required- standard (93 unique glyphs, cf. ~1/3 of dupes in your incomplete set [20 dupes / 62 glyphs for the moment]). I am sure you can add at least several punctuations. Until this -ideal- completeness, it's not (qualified as) a -text- font, and despite of already quite readable glyphs, their duplicate(s) make the wole a little illegible, as you titled yourself (too bad, but now you know more about how to overcome this very difficult/expected situation).

Thank you for showing us your 'mapping' (i.e. your selected 2x4 dot-matrix glyphs), your budding skill in minimalism and confirmed perseverance in general!

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Now an exclusive tip for the most advanced readers/experimenters: I could design a 2x4 variant (of my own 2x4 - itself derived from my 2x3), with all the columns used! (which was the 'Holy Grail in the Kingdom of Monospace Types'…) [Striped RGB works there too - with the only valid world record in this field b.t.w. - and I love its even 'type color' - because all the characters are effectively 2x3, this can have a lot of applications in design.] This tiny monster is one of the rare exceptions of my -unreleased- catalogue. :-)