As mentioned in
the 2003 3DNA NAR paper:
The stacking interactions are quantified in 3DNA by the shared overlap area, in Å2, of closely associated base rings, i.e. the nine‐membered ring of a purine R (A or G) and the six‐membered ring of a pyrimidine Y (C, T or U), projected in the mean base pair plane.
So 3DNA, as is, may not provide a sensible value when a non-standard base ring is involved, such as your 3-ring linker. However, you can have a look of the corresponding step in the "stacking.pdb" file, and write a purpose-specific script to get your job done; after all, mathematically, it is all about getting the intersection of two polygons, and then calculating its area.
If you want to go further along the line with 3DNA, please make your problem specific. By using your case as an example, we may extend 3DNA, or at least provide a use-case, in ways potentially useful to other users.
Xiang-Jun