The problem is definitely foldover, and the reason is that, for whatever reason, the horizontal retrace is happening too slowly. The retrace speed is determined by the inductance of the yoke, capacitor C12, and the inductance/capacitance of the flyback transformer.
The yoke is probably fine since the rest of the picture looks fine, so concentrate on the other two. Of those, the flyback is the more likely failure but C12 is easier to replace, so start with that.
It should be 0.033uF (maybe slightly different on some models), and I would use a part rated at 250V, or more if it's labelled that way on the part you're replacing.
What normally happens is that when a line of video finishes, the HSYNC pulse goes low and transistor Q2 switches off. At that point, the beam is at the right-hand side of the screen and there's several amps of current going through the yoke. When Q2 turns off, that current charges up capacitor C12, in the process moving the beam back to the left side of the screen for the next line. That whole process is supposed to finish well before the next video line starts, but if C12 (or the parasitic capacitance of the flyback) is too large, the retrace will happen too slowly and the next line of video will start before the retrace has finished.
It shouldn't be related to the positioning of the yoke or the magnets. There are a few other possible failure points on the analog board but C12 and the flyback seem like the most likely.
