When I first started using DesignCAD, it was $279 for 2D only, and $495 for 3D, and the 3D part was in DOS. I no longer use it, since I use AutoCAD at work, but imo it's one of the easiest CAD programs to learn, and is very powerful. The pnly problem you might have is getting it to export files in a format that MeshCAM can read. MeshCAM can read .stl files, or .dxf's. But, the .dxf's can only contain 3D faces, which DesignCAD may or may not let you do. If it exports .stl, then there should be no problems at all. Unfortunately, I'm not sure that it does. There are conversion programs that should work though, and they are inexpensive. This one is $20.
http://www.micromouse.ca/You can download a trial of both DesignCAD and MeshCAM, and see if they'll work for you. (I know what you said, but for the price it's worth a try. I am a MeshCAM user, btw, since the very first beta. Nothing else comes close for the price.
Also, like I said before, you may find it difficult to produce the shapes your after using DesignCAD. If that's the case, then Rhino would be a better choice.