One other option that hasn't been mentioned is that for each passenger on the PNR in question, you can choose whether or not to request a complimentary upgrade to Comfort+ and First accordingly. When you go to your trip in delta.com using a full deskop client, not mobile - scroll down past the flight and seat selection info. Down below there, you'll find the section about complimentary upgrades. Check and uncheck the boxes and save. Easy.
Now for whether those settings are honored by Delta IT is another matter, I haven't tried having different upgrade requests for different passengers myself. I never liked the idea of splitting PNR, but that doesn't seem to be a bad route either.