I have found that my trunk rack does not properly accommodate my new FS bike (Marin Rift Zone). Can't quite figure out the physics of it, but one side (the "high" end) of the bike seems to work its way off the perch on longer drives.

Regardless, the solution seems to be to use one of these top tube adapters that spans between the stem and seatpost to create a faux horizontal top tube on the bike, making it "level" in the rack.

Yakima "Tube Top" is one of several of these that all seem to work about the same way, i.e. with a hook around the seat post just below the saddle clamp at one end and the stem or headset at the other.

My question is, does the suspending of a portion of the bike by the saddle/seat post "threaten" to potentially damage the dropper post?

I'm not sure what the precise mechanism is that limits the upper travel of a dropper post (although I can imagine several) and whether that might be damaged by being placed in tension or "pulled on." In the other direction (compression), of course, the dropper tube will support several times the bike's weight and in dynamic conditions, I just don't know about tension.