One small step at a time! This is beginning to look like a good thesis project for mega-geek (with all due respect and hats off to the species) doing a university course in kinetic physics, not a middle aged chap with a distant interest in the subject and a hobby of fiddling with C++ every now and then, current schedule permitting, who once upon a time took an automobile engineering college course.
That said, I do see what you mean. Precession of the spinning shell IS going to cause it to cant sideways as its nose dips to follow the trajectory curve, which will present a side of the shell at an angle to the relative airflow and generate a side aerodynamic force, which in turn will cause the shell to drift, in the direction of its rotation (right hand spin, right hand drift). All of that is going to mean calculating the principal moments of inertia of the shell, which first, is going to define the angle of difference you mentioned of the shell's center-line to the trajectory flight path (as its aerodynamic longitudinal stability characteristics tend to try and keep it aligned with that flight path), then the magnitude of the side angle induced by the precession. In essence, it is not difficult to calculate the number of spins the shell is theoretically going to do during its voyage, but the effects are going to be a different kettle of fish. However, the effect of precession is a 3D consideration, and my model is (as yet) 2D.
That does not discount the effect, however, of the shell's resistance to change its orientation, because of the gyroscopic stability of the spinning, relative to the changing flight path, even on the 2D planes, generating that "angle of attack" which will create the aforementioned lift. The "lift" (actually, total resultant force) is also going to cause some additional drag (induced drag), which basically is going to be the sine of the angle of attack times that total resultant force, at least in this case of a symmetrical shell. The lift itself is no problem to calculate, but again we come back to the problem of its coefficient. And I am still stuck on the changing coefficient of drag due to compressibility at supersonic speeds. I have dug out a couple of books and am delving through formulas, with calculator and pen in hand. Good way to use up my one day off, when there were things to do around the house. This is going to make me popular...