A while ago, I discovered that you can create “fixed joints” between the table and the base_link of the robot arms that can be “excluded from the articulation”. In order to get Isaac Sim to recognize both articulation roots on the arms, you have to select to exclude from articulation for these “fixed joints”. I have quotes here because while the these fixed joints are connecting the table and the arm, when you exclude them from the articulation, they become a maximal coordinate joint as specified here:
It is not ideal, but it seems to be doing the job for now. The original question still stands though with the constraint of having a true fixed joint between the arm and the table.