Gparted will work fine in XFCE, it's not _that_ reliant on GNOME if memory serves me right (in fact, it seems to be just another GTK application, like most of things that you'd use in XFCE).
Alternativelly, there's parted, which does the same thing using a command line interface.
Also, you could:
0 - dump /dev/sda12, /dev/sda13 and /dev/sda14 data using tar, rsync or even cp (or just ignore this, as you said they don't have anything yet)
1 - boot with a livecd (or umount /dev/sda12, /dev/sda13 and /dev/sda14 if you feel brave enough to change the partition table with your system running
2 - fdisk /dev/sda and delete /dev/sda12, /dev/sda13 and /dev/sda14
3 - recreate them, with the proper sizes
4 - format and mount them
5 - restore the data
6 - reboot into your slackware (if you used the livecd)
As for the LVM, it's far easier than you think. In fact, it requires less than 10 commands to set up LVM during Slackware installation (see README_LVM.TXT) and it'd be much simpler to resize the partitions (umount, fsck, lvresize or lvexpand or lvreduce, resize2fs, mount), not to mention that it could be done without the need to touch the partition table.