I assume that PSXITARCH is capable of supporting and communicating with connected USB devices. If so you can try the following.
1. Get USB thumb drive, format it to FAT32 and copy the games to it.
2. Boot into PSXITARCH.
3. Start a terminal and get root access (sudo su).
4. Insert the USB thumb drive into a free port on the PS3.
5. Type "fdisk -l" and in the output identify that USB thumb drive with the games (you should see it based on SIZE and the FAT32 filesystem). Take note of the path of the partition on that thumb drive. It should be something like /dev/sdXX where XX would be either a1, b1, c1 and etc (depends on how many other drivers and partitions the system has detected).
6. Mount that USB thumb drive partition with the games to mnt with "mount /dev/sdXX /mnt".
7. You should now be able to open the file manager, go into the PSXITARCH root / and open the "mnt" folder there.
You should see the game files there. You can copy them around now hopefully.
After you're done you can unmount the USB thumb drive with "umount /dev/sdXX".
All of this requires Linux knowledge though.
Here is another howto:
https://linuxconfig.org/howto-mount-usb-drive-in-linux