I used 1.11 to back up all of my first season STNG disks, and had no trouble at all during playback. I don't know if maybe there's some kind of incompatibility issue between your decrypter and DVD2ONE (it happens), but here's the method I used:
1.) Use DVD Decrypter in FILE mode, copy all files into the folder of your choosing.
2.) Run main VOB set through IFOedit to remove unneeded audio streams (I removed the 5.1, since it helped with the image quality). Piece back together with untreated VOBs and click "get VTS Sectors."
3.) Test project using IFOedit's "DVD Play" button. Be sure that you don't still have your original disk in your player, or IFOedit will simply start playing that -- leaving you with the false sense that everything turned out alright!
4.) If all works well, fire up DVD2ONE and let her rip.
Make sure you put both VOB sets into your project (since all episodes reside on 1 VOB chain, it's tempting to only use the ones you stripped... however, you'll wind up with navigational problems if you don't use the VTS_02. chain, as well).
Hope this helps!
Edit I just became aware that DVD Backup is a Mac software... is that correct? I'm about as dumb as a post when it comes to Mac stuff, so I really can't make any suggestions toward that end. I don't know if there's a compatible version of IFOedit that you can use, since I've only tested and used the PC version. But, nonetheless, what you're trying to do is possible.