In reply to Correcting a glyph's hinting:
"...the solution to your problem is really quite simple: don't use the font at that size."
Wouldn't that be nice!? Redesign your pages, or switch types for font sizes that work. . . if one is not crude media savvy, sometimes listening is best.
Also,
"...the glyph itself is probably 14ppem high..."
...ppm refers exclusively to pixels per em. Once you start talking pixels per cap ht, e.g. it's no longer ppm, but simple pixels.
"If you use other instructions, the Control Value Table in the font has to be rewritten"
Deltas will work if placed correctly. The cvt might be used, but because there is often slight variety in the optical centering of middle strokes, one can alternatively interpolate the top of the mid stroke between the glyph's y min and y max, set rounding to sround 73 and mdap it, avoiding the cvt, while never having the mid stroke too low...