Hello,
I'm pretty sure I know how to solve your issue:
I took a bit of time to think about your problem. If I understood correctly you have a sphere with some Yaw, Pitch and Roll then you want to apply some rotation (Delta Pitch) and workout the resulting angles.
To achieve that I'll use matrices, simply put I'll compute the 3x3 matrix of the resulting rotation (yaw, pitch, roll then new rotation) afterwards working out the new Yaw, Pitch and Roll can be done by applying this rotation to the base vectors and analysing the results.
I'm new on this site but I'm very familiar with such angle calculations.