Most plasma and lasers have a ''tolerance'' inside it to treat minimal gaps as joint rather then gaps.
There's also a setting inside SolidWorks when you do ''Save As'', go into the DXF options and set them to merge together.
Also, DraftSight's zoom is not all that reliable when you go deep into the zoom, have you tried using the polyline command to try and merge them all together and see if it closes?
Your suggestion of changing the SolidWorks setting to allow for merging an exported drawing's separated lines appears to have worked. Thank you so much!! Really helps.