Deflection coils come in pairs; horizontal deflection is accomplished by coils above and below the neck of the tube, and vertical deflection is done by coils on either side. The intent is to create a uniform field between the coils, so the two coils in a pair are wired together and driven with the same signal.
Coils can of course be joined in series or parallel, and the failure modes differ between the two. With series coils, deflection tends to either work or fail entirely. With parallel coils, it's possible to get the kind of 'half-way' fail you described. You wouldn't think a simple, non-moving thing like a deflection coil would fail, but evidently they can suffer from both shorts and opens.
So you might want to fire up the soldering iron and separate the leads of the left and right coils, and continuity check them. If the two sides ohm out differently, your problem is the deflection yoke; the two coils should have the same DC resistance. Not sure how you'd go about resolving that problem, but at least you'd have isolated the problem and wouldn't have to dig into the circuits.
See Bernard Grob's Basic Television Principles and Servicing, (4th edition ~1975, probably out of print). There's a chapter on vertical deflection circuits that specifically mentions that fail mode with vertical deflection.