I calculated out a redundancy of 1.36 bits per glyph. Taking that at face value, it would mean the space of possible glyphs is about 2.5 times the space of used glyphs. Is "between 2 and 3 times as many letters as there currently are" congruent with what you consider "tons more information"? If so, we haven't actually contradicted each other on any matters of fact. Just on matters of what it subjectively means to have "tons more information".

1 bit of error correction for 5.6 bits of information sounds pretty good.