[Electronic M]

I'd sub the tubes first. If you are set on adjusting the linearly control make sure to monitor the hot cathode current while doing so and avoid running it too high.

There's a possibility the set is fine, and the problem lurks in your cable box. I've seen systems that stretch only the edges of 4x3 programs to fill a 16x9 screen(resulting in a 16x9 image with good center linearity and lousy side linearity)...it is entirely possible for the cable box to be doing the opposite (non-linearly smooshing a 16x9 image into a 4x3 frame.
Do you have an old-school hardware based TV test pattern generator that predates broadcast HD?... If so hook it up to the TV and see what a grid pattern looks like...if that looks linear on the set then your cable box is probably the problem.
Another check would be for vertical lines or stripes of varied brightness that show up on both program content and blank raster....if beam velocity changes much across the screen (which is the definition of non-linear scan) then brightness will vary too...the longer the beam dwells on a spot the brighter the spot becomes (as you probably will learn if you play with a scope).