You can use BTM-2015 or its successor BTM-2017 to handle the three-game qualifier to determine the top 16 to be put into the double elimination bracket, but beyond that, everything would have to be done manually.
Set up your tournament as a three-game, with handicap set appropriately if used, and run a report after the three games to determine the top 16.
However, the double eliminations themselves, seeding, and tiebreakers if necessary, would be all manual. I'm not aware of any CDE products supporting eliminators of any kind (outside of eliminator brackets, but that wouldn't apply here).
Always check, download, and install the most recent update of your software to ensure that issues may have been corrected.