The problem is that you have to write at a particular font size or else the third dimension distance is ambiguous. In 2D writing systems, a letter 'S' drawn on inch high is as comprehensible as the same letter drawn a half inch high. But with your system, the small S looks almost the same as a large S with a smaller Z-height.
The distance between the two tips of the pen apply a fundamental scale to the text which prevents you from using it to make a tiny footnote or write a huge poster.
This confusion between Z-distance and "font size" would make it tough to recover the 3D data if you don't have some absolute scale references.
A related issue is that the Z-distance can only easily be read back when the pen is known to be travelling at 90 degrees to the tip separation - so letters like 'O' allow easy conveying of Z data - but either I's or _'s or /'s do not (depending on what convention is chosen for the pen orientation). That can perhaps be fixed by careful glyph choices, but eliminating a wide range of glyphs that would have ambiguous Z-height might easily erase the extra information content that could be encoded in Z.
I'd also point out that using an easily obtainable pressure-sensitive digital pen in a system like Photoshop or GIMP allows you to convey the third axis using pressure (which could trivially be translated into Z-height using a spring in the shaft of the pen) - but without the problems introduced by having the two nib system. In those software packages, you generally map pressure onto line width, which (with an appropriate 'brush' shape ) produces very similar results to your solution. Using a system like that in practice produces similar issues of legibility for small and large 'font sizes'. When writing in a 'brush script', you need to change the size of the brush depending on how big you're planning to write - or the lettering rapidly becomes incomprehensible...and that's even when the information is conveyed in the 2D shape alone with pressure not being a part of the 'information content'. Your system has that - and worse - to contend with.
-- Steve