Try this: Use Gaussian blur on the portion of video that has shimmering. You can also use blur on the whole video if you do not want to spend time fixing that shimmering. The 4k video is too sharp and the edges must be reduced to a resolution of say 720 x 240 lines to work well on a standard dvd.

This post may help: https://www.avforums.com/threads/shimmering-vertical-lines-in-hd-footage.1538406/ .

Please help us a bit:
What are the format specifications of the Canon 4K files you used as input,
What are the project specifications you used like the timeline frame rate, timeline preview color etc. (they may have nothing to do with the problem but might give an indication why preview went ok and the final result not),
what are the DVD specifications you used?
Did you create the DVD with PD or did you use another tool, if so what where the file specifications used?
Did you try the DVD with computer software and/or did you use a DVD player, if so, anything different like between PAL and NTSC.
Where the input files 16:9 and was the DVD too.
Did you use the hardware acceleration and/or enable hardware decoding, which GPU was used?
Etc. Screen shots will also help.

The other issue is that you're trying to cram 4K content into HD DVDs and that will always create some level of artifacting. For the best quality you should be using Blu-Ray discs if you need physical media.