Mark, i have been following this thread while trying to remember what i used on my pointerless knob. i'm pretty certain i used Simichrome and a dense woven piece of flannel-like cloth. Simichrome is the classic German very fine grit aluminum polish, readily available in the US for at least 6 decades. as an aside, i've used Simichrome on the speedo/tach clear lenses with excellent results. on the lenses, i follow the Simichrome with Meguiar's clear plastic polish.
your knob appears to have some somewhat deep defects, at least on the top; probably degradation from some sustained exposure to uv rays, temperature extremes and moisture.
i don''t think these plastic products you are using are aggressive enough, especially applying with a toothbrush. i guess what i would suggest, i see no reason why you could not give a trial of 1500 grit paper; start on sides and see how the knob material responds. i am confident the material that knob is made of can be worked. or, if you have an old black knob you don't care about, experiment with fine and if necessary, coarser grits of paper.
i also have polished various types of plastic using fine rouge and a polishing wheel/pedestal motor. one MUST go lightly polishing plastics using a wheel, but the results are generally excellent.
i've known a couple fellows who've taken a new pointer type knob, removed the pointer with a mini-file and then shaped the remaining material atop the knob into the desired contour with the same file.
before and after pics of 232's knob. looks like mine may not have been as weathered as yours.
and..... the two outer dots are no longer red.... ! black like they were original. once in a while i do stupid things.......