It took me a little while to do the conversion, but in the end it worked pretty well.
To start with, I used the converter from 1.1 beta; I'm not sure if the 1.3 converter is out yet (it wasn't a week ago), but that one seemed to work fine.
Second, I got similar errors to you. First I copied the entire original yabb directory (the one containing the Members, Boards, etc. directories into the same directory as my YaBBSE installation. Then I chmoded everything in that directory 777, then ran the converter (from the same directory as the YaBBSE install). At that point, it ran pretty much without a hitch (took a couple of minutes).
I don't know if chmoding everything in the original directory would have worked or not; I didn't try it since I didn't want to screw up permissions in case the import failed. For what it's worth, I also used relative paths (./whatever) when giving the converter instructions, although I don't know if that mattered either.
On a side note, the conversion seemed to loose some people's birthdates, and several people apparently (though I didn't see it myself) had to try logging in several times before it would work the first time they used the new board. I don't know why.
Hope that helps, but if you're still stuck I'd be happy to see if I can figure out anything else I did to make it happen.