There’s all kinds of DXF to SVG to DXF to whatever converters out there. I use em all the time to migrate stuff in AutoCAD. Granted it’s not perfect, you end up with a lot of splines and junk you sometimes can’t use, but for the most part it works.
Yes, I translate DXF to SVG using Inkscape. It works well and it’s a reasonable workaround. Takes a couple of minutes per print to load, adjust, and save out. I never get my parts right the first time out, so after about 2 to 4 times going back and forth it gets tedious.
This sounds like a good justification to invest in learning Inkscape (or a vector program of your choice), maybe? Your design was actually a fairly simple one for this, would have been an excellent project to get more familiar with it. It’ll definitely save you time long term.
Also I don’t know about draftsight, but if it puts out PDFs, the GF speaks PDF…
I haven’t tried it with Draftsight as I only have the free version, but SolidWorks saves DXF to PDF and the GF imports them as vectors. I suspect @evansd2 is correct and you could just export from DraftSight to PDF and straight into the GF. Always worth trying.