I think the FW version is 1.1.3, not 1.3, but in any case you should be able to go back to 1.1.2 if you ever downloaded it in the past.
To do that, try another Restore but this time hold the Shift key as you click the "Restore" button. You'll see a pop-up window showing prior versions of firmware that are already on your computer. If 1.1.2 is shown, you can select that and it should install. Note though that if your iPod came with 1.1.2 you won't have it on your computer. Your computer will only have firmware which you download from Apple by doing an iPod update from within iTunes.
If you want a fresh copy of 1.1.3 you can try this if you're a Windows user:
1- CLOSE iTUNES and then use +My Computer+ to locate the folder:
C:\Documents and Settings\ +(your Windows account)+ \Application Data\Apple Computer\iTunes\iPod Software Updates
2- Look for a file with the .ipsw extension that is named something that looks like "iPod1,1_1.1.3" in the name (sorry, don't recall the exact name).
3- Don't delete this file, just move it to another location that you'll remember.
4- Start iTunes and connect your iPod. You should be notified that a new firmware version (1.1.3) is available. If you choose to Update, you'll re-download a fresh copy for your iPod. I always recommend the option to "Download Only", not "Download and Install". I then install the firmware after it successfully downloads by pressing the Update button again. I do it this way because I don't trust the way Apple handles the download-to-intall transition. +(I do something similar for iTunes updates too -- download the install file direct from Apple, then install manually)+
5- Once you've updated to a new copy of 1.1.3 you can delete the .ipsw file from step #3.