I have a Kyo 7135 and am also using Slackware 10.2, although it is with a 2.6 kernel and not a 2.4 kernel. I am using JPilot (which uses pilot-xfer) and it works very well, either through serial or USB. So at least you know it is possible.
It probably isn't the permissions, but have you checked ttyUSB0 and ttyUSB1 so that they are read/write for the world? What is the command you are typing in to initiate pilot-xfer?
I assume you are initiating the sync from the 7135 first, waiting a few seconds, and then issuing the pilot-xfer command? I know that when I do a USB sync, it takes 2-3 seconds for udev to "create" the device before I can sync. Under 2.4, I don't think you have udev (IIRC devfs is what is in 2.4 by default in Slack), so the device may be there regardless.