Rendering export of converted PAL video causes some pillarboxed scenes to waver left and right?!

I assume your video is 720x576. if that is the case, your video is at PAR (Pixel Aspect Ratio): 16x15 and not PAR: 1x1 (Square Pixel) and your Display Aspect Ratio (DAR is 4:3).
1920x1080 is a resolution for Square Pixel for DAR of 16:9.

You got two options.

  1. “Select Width” → 1440 and Also select Square Pixel Type. this would be much more natural to your 720x576 4:3 Video.

image

  1. the Other option which in my opinion is much better and the petered method would be to De-interlace your video (if needed) and convert your Video to Square Pixel both in “Hybrid” powerful free tool, PAR: 1x1.
    (which result a 720x540 output resolution). and in Lossless format like FFV1.
    Then import it to TVAI and select x2 Upscale option.

you can see a Picture here for PAR conversion.
for lossless encoding in Hybrid, read here.