YMG,
I have an idea for eliminating the bogus exterior TIN's...
1) Prior to a TIN network being built, provide a routine for the user to construct a straight-line polyline (as a boundary) by their valid exterior points. If it is not a single polyline (by messing up and restarting), have the user merge all of its polyline segments.
2) Prompt the user to select the boundary and indicate an offset direction and distance for a temporary offset polyline (by a foot more-or-less) to its outside.
3) At activating the TIN, the boundary can be exploded to be used as breaklines. The temporary polyline can be moved to a layer that is frozen.
4) The TIN proceeds to build.
5) At completion the TIN's that are intercepted (crossed/fenced) by the temporary polyline are deleted.
6) Delete (or freeze the layer for) the temporary polyline.
Note: Before deriving this scheme I had looked at Xshape to force it to not violate breaklines. Rather than possibly damage Xshape, I thought that this alternative might work just as well.
Rick