OK - the enclosed video shows how I would do this
1) I would create a View Filter for the data that I want to Export
2) If I want to exclude some of the View Filter Data from the Export I would create a selection set of the data to exclude and then in the View Filter / Selection Set I would pick that selection set and exclude it from the display
3) So On screen now I can see all of the data that I want to export to the field systems
4) I run the Design Manager, Pick the Design Type - you stated 3D Linework - and then select all of the data that is visible and add it - it tells me that some data was skipped and some was added - so to determine which was selected I would de select all the data and then hit the Select Button - that will show me what was selected for export - if I want to see what was not selected (Skipped) then I would use the Invert Selection command to show me what wasn't selected.
In my tests I used lines that had undefined elevation (?) and Zero Elevation (0.000) and Elevation of 0.001 and a line with 0.0001' (which is sub mm) - the lines that were ignored were lines with ? and 0.000 but all lines with 0.0001 or or.001 were selected and sent. So as a work around for 0 not working, you can set those lines with valid 0 elevation to 0.1mm high and they will get sent to the machine files.
I am not sure if this is a TBC issue or a Machine restriction - it could be that the GCS or Earthworks system assumes that Elevation 0 is undefined in which case this is why TBC behaves the way it does (and this is my guess actually because we use a CTCT generated library to manage the Machine Data exports and that validates the data and flags unacceptable data items)
Hopefully the video helps
ALan