How to design a near vertical take off airplane?
Yes that is conceptually correct. You might have to mount a huge area, since lift is proportional to $V^2$.

Issues to resolve that I can see:


The craft would be relying upon aerodynamic forces to maintain attitude, which will be very ineffective at 20 mph. A secondary pressure relief valve system for attitude control would be advisable.
Landing at 30 degree nose up will be not easy from ground view perspective, and for landing gear design.
Ground effect will change the attitude of the craft if not carefully designed.
A wing that does not stall until 30° will be a tall order, and landing at the brink of stall is not advisable, you'll need some margin.