I just finished doing it last night and my method may not be pretty but it worked.
First: I copied the message, members and board folders from my existing server to my hard drive.
Next: I built a basic Yabb 1.3.1 on the new server and dropped the contents of the messages, members and board folders in there.
Next: I built a basic 1.5.5 YabbSE board on the new server and used a Y1G converter to drop my 1.3.1 into an SQL database. Then I processed using the SMF converter.
Like I said, it wasn't pretty but the converters worked like a charm.
The only issue I had was at the end of the YabbSE -> SMF convert was getting the settings.pl into the settings.php. I tried the process twice and it wouldn't work.
The third attempt was to remove then recreate the YaBBSE database completely from scratch, run the Y1G convert, then the YabbSE -> SMF convert; leaving the settings.pl alone. For some reason it seems that telling the YabbSE -> SMF converter to clear everything out didn't quite clear everything and I got the same errors as I did the first time.
That worked and I have everything in.
-Jazhawk