Greetings Thad,
You could select the chains you don't want to cut and remove them like you were doing. That takes too long, but the only other way I know would be to edit those files. That is something you'll want to be able to do anyway. Most of us here don't deal with files that have construction lines or title blocks. You will want to get some type of CAD program that will allow you to edit files because sometimes drawings just must be tweaked. Sometimes scaling gets lost. In one of my files the object was 3" across in CAD but when I saved it the object measured 0.07" across in CAD. I spent a few hours trying to figure out why I couldn't pocket it with a 1/4" end mill before I noticed the scale bar in the upper right hand corner. I opened it again and it was the version of AutoCAD LT that did it when I saved the file as ACAD R12. Sometimes lines look like they meet (closed chains) but they don't when you zoom in... LazyCAM does not like overlapping or redundant entities, open chains, or some types of arcs. There are some great and yet inexpensive CAD programs out there like TurboCAD, Rhino3D, DolphinCAD, etc. Many can be found with evaluation periods to try 'em out. Hope this helps. Happy cutting.