When looking for a 3.1 rom for your A600 remember that it was the same rom for the A500, A1500, A2000 and A600. So if you see a 3.1 rom listed as being for any of these Amigas it will work in the A600.

Failing that you could get someone to burn you an EPROM of Kickstart 3.1. Zetr0 did this for me for my A600 and it works fine.