After using the script ‘Download Bibliographic…’ included with DT3 and seeing it fill in the missing DOIs nicely (well done), I executed ‘Export to Bookends’ via the menu. While the script did export the references to Bookends, it left out all the DOIs. Only a few authors (field) made it into Bookends. Which was a bummer.
What went wrong? Perhaps the sheer amount of papers (663) was too much for Bookends to keep up. ¯_(ツ)_/¯