I'm not sure that the description for a pointed on-axis-spinning projectile is a good model for the reasons for curving of a spherical projectile.
The curving of a baseball has been studied in varying levels of detail and sophistication and is a good model. Surprisingly, the physics experts had been naysaying the existence of the curveball even quite recently. link A simple starting point can be viewed here link The low pressure wake of the ball is uneven because of the spinning and it cause the ball to move sideways. (Magnus effect) link
If the axis of spinning is the same as the direction of flight, the direction of the forces is symmetric and doesn't curve the ball. If it is not, then it will move sideways. So patching a ball and having the patch grab the rifling to start on-axis spin is a good thing for accuracy.
The flow of the air over the ball can be described as its Reyolds number, which is basically whether the flow is smooth (laminor little force generated) or turbulent.
A baseball (cricketball) or a unevenly cast musketball will also have stitches on its surface that will significantly affect the flow of the air over the ball. How you hold the ball and snap your wrist, changes what happens. (that is why you can throw a curveball, slider, screwball or be a spin bowler). The axis of rotation is not the same as the direction of the projectile, so it moves sideways, rather than just a tiny bit faster or slower.
One feature of a baseball "curve ball" is the late breaking pitch, which players and fans know and see but "experts" say was impossible. (The same thing happens with late curving bananna kicks in soccer). In this case, what happens is the ball slows down as it travels (due to air resistance) and near the batter, one side of the ball the sum of rotational & forward velocity kicks the forces from a laminar to a turbulent flow. There is a late change in th forces and the ball "breaks".
Another aspect of all this is that one way to lessen the effect of uneven air pressures is to have a lightly pitted surface on the ball, so the sideways forces do not change as drastically. That is why cannon balls were not rubbed smooth- they were less accurate that way. For the same reasons golf balls are dimpled rather than completely smooth like ping-pong balls (where controlled erratic flight is a sporting virtue).