Your problem stems from the "current switches" of the XR2206, not unlike the crossover distortion of some op amps. You only noted the issue at the predominate point, but if one looks at the signal at the opposite polar transition one can see the same issue at a somewhat lesser degree. The real issue is with the deviations from the manufacturer's recommended configurations.
I'm thinking that what one should be more concerned with is first, following the datasheet recommendations, and second the noise superimposed on the sine output as displayed.
Is the MO input (pin 3) bypassed properly? There should be a 1uf-10uf tantalum cap. there as well as the proper configuration as outlined in the datasheet.
You say the symmetry pot across pins 15 & 16 has no effect. Have you tried a 25k 20 turn cermet pot to get the desired results?
In conjunction with the symmetry pot, have you tried the recommended 500-ohm with at least a 10 turn pot for the THD adjust between pins 13 & 14? One may have to make adjustments to the amplitude also to ameliorate the effects of the crossover spikes, which should only be apparent in the upper frequencies.
Another note of departure from the recommendations is the 680pf cap used for the upper end frequency output. That would indicate to me one has constructed the circuit on a breadboard. That is right around the value needed to get up the hill to 1Mhz on a breadboard owing to the stray capacitance inherent with that construction. One cannot trust all the results observed as credible when implementing that device on a breadboard.
Before I forget it, get rid of that 100nf cap between pins 4 & 12 and put one on pin 4 to ground and another from pin 12 to ground, and you just might get a cleaner sine wave sans noise if the other items are dealt with.
If the device is constructed correctly, there will be no need to for add-on circuitry, for which to make corrections to meet the THD limits specified. Been there and done that with the 2206 many times with my students waaay back when.