A yoke on the tube means magnetic deflection. Maybe there is a shorted turn or a break in one of the yoke coils? That can cause vertical/horizontal collapse, but I don't think I've seen it cause rotation. When you say "twisted 10 degrees from plumb", that could mean rotation, or it could mean a geometry problem like trapezoidal or pincushion misalignment. The geometry is controlled by dynamic circuits that change the deflection timing.
The other part of the magnetic deflection system is the purity magnets for color tubes. Those are placed around the neck, sometimes a pair of ring magnets are used, other times they are small disc magnets stuck on plastic pegs. They don't rotate the picture, but if misplaced they cause color smearing.