Here's the promised update. I still have ULD on my primary line according to the rep and the "My Verizon" website. Don't ask me for the steps because I tried doing it online and had a bunch of weird things happen. I ended up just calling customer service and a rep helped me with the first part (activating on dumb phone line and then putting the dumb phone back on that line while having the iphone sim go into "sim aging") and the second part (activating the iPhone the next morning after the sim had reset onto my ULD line).
So yes, at least for me, I was able to transfer my upgrade eligibility to a dumb phone that was not yet eligible and keep my unlimited data.
Thanks so much for updating us. So after the online system gave you problems, you called CSR and said I want the phone activated, then taken off, and the sim put in aging?