I know you're invested in the 'perfect pitch' framing, since you mention that you have it in the family. Since it seems like your goal is to have this be a useful and accessible educational tool for those breaking into music, I would highly recommend pivoting this to have a strong focus on relative pitch, and specifically _intervals_, instead. Knowing how to distinguish intervals is both more accessible, and also much more useful for actually playing and creating music. As is, this tool clearly deprioritizes intervals with the fixed piano-key input and melodies in a key other than C. This will really only help one get better at this specific game.
If you haven't already, give Earmaster a try and see how they approach it - it's one of the most referenced and well-regarded training apps on the market. Earmaster, and others like it, start with a focus on relative intervals, then expand out from there to enhance instant recognition and memory of relative intervals across a melody - but the focus is almost never on absolute pitch 'across the piano'.