Personnally I prefer grub legacy or 0.97 to grub2. It is more simple to modify.
#installpkg grub-0.97-i486-9.txz ,so without using a network how do you install the patch?
With grub-0.97-i486-9.txz you do not need to install the patch. It is included.
From there you can use grubconfig to install the menu.lst on sda2 (antix) or on sda3, and if grubconfig provides the right menu.lst entry for slackware (what it should do), you should be able to boot slackware.
Was there some menu.lst entries for /boot/grub/ on sda2 for antix? If there were make a backup of them outside /boot/grub of sda2, to use them later, if the grubconfig generated entries are not appropriate.
Then using cli mode with grubconfig command access the dialog:
/dev/sda2 (for antix partition)
4)grub is mbr:
Then reboot, it should boot slackware and maybe also antix. If not you need the appropriate entry in menu.lst for slackware and/or antix.
Here is a model of menu.lst entry grub legacy for slackware, see post 2:
kernel /<vmlinuz_filename> ro root=/dev/hda<partition>
Are these partition on hard disk or are they on usb? (I have the impression that you are talking about a hdd installation) Where are located the vmlinuz_filename and initrd_filename?