Original poster here. I still check the forum regularly, so don't worry about the age of my posts.
I ran into similar problems importing DXF files in VCarve. Ideally, we would want to smooth out the vectors before trying to make a path, since the
tiny, tiny variations won't matter at all on a physical medium. Those are far more precise than, say, the angle on my bit. Unfortunately, most tools don't have an option for this, so we need to make do with very large vector files.
The next step is to combine individual tiny, open vectors into big closed vectors (loops). I found that if I selected everything and tried the automated function in VCarve, the system would freeze for a while and then crash. To get around this, I only select so many groups at a time, run the function, then repeat. Eventually, I can select everything at once and run it, just to make sure I didn't skip anything. I had to do this for the successful image I posted, which consisted of several very long loops.
The last step is to create a tootlpath and output g-code. I rarely run into issues here, but a week ago I found a case where VCarve didn't want to create a toolpath with too many tiny vectors in it, so I created a series of toolpaths then combined them into a single g-code file. If you find the size of the g-code file to be too large, you could create several smaller ones and run them in sequence.