Ok, I'll answer as a font designer: I think you need to have the font designed or design it to meet your requirements.
In the image you are submitting of what you're looking for, the lowercase "g" and "y" (etc) are not typographically "correct", meaning, they do not respect typographical conventions for lowercase letters and are not pleasing to the eye of typographers, and would not validate.
So, either have a font designed (or design it yourself) because I cannot see what a lowercase "g" - for example would look like and still be agreeable to read.
Another option would be to use "small" capital letters instead of lowercase letters (check out a font like "bank gothic" or "Copperplate" to understand what I mean).
Clearly, the readers would perceive a difference in font sizes (you could even use a bold font for the capitals and a regular smaller font for the lowercase), but each glyph would look "good" and acceptable.


If I had to design a font that meets your requirements, I would probably use "standard" lowercase glyphs for every letter that doesn't have a descender (a, b, c, d, e, f, h, i...) and use a minified capital letter for the letters with a descender (g, j, etc). But you would soon see that for example a small "Q" and a "d" with an ascender would not look like they belong to the same font unless they are designed to do so. And that would mean making every font with an ascender (b, f, h...) look also like a small capital...
