their is one more option but im reluctant to post it on here because its bordering piracy, however saying that if you had paied for it originally...............................
im assuming you have the original singstar?
back it up to an external hdd.
here is the fine line im walking, find the singstar volume that has the songs on you PAID for and download it (lots of places and sites google ps3i*o

)
back it up to external hdd, use your pc and go into the game folder that has the songs you bought and look for the files named pack0.pkd, pack1.pkd ect ect
copy those files to your original singstar backup you will need to rename them first so they dont conflict with whats in the folder already so say your original backup has pack0.pkd, pack1.pkd you should rename your new songs to follow suit like pack3.pkd pack4.pkd and then just start the original singstar and the extra games should show up in the game menus.
I WILL JUST POINT OUT FOR THE WINGERS ON HERE I DO NOT CONDONE PIRACY EVERY GAME I HAVE BACKED UP I OWN THE RETAIL COPY TOO AND I HAVE GREAT RESPECT FOR THE GAME DEVELOPERS THAT SPEND MANY YEARS AND MILLIONS OF ££££££s BRINGING US THESE GAMES. HOWEVER SAYING THAT I ALSO BELEIVE THAT PEOPLE ARE ENTITLED TO WHAT THEY PAY FOR AND THAT SHOULD NOT BE TAKEN AWAY BECAUSE SONY DOESNT WANT CUSTOM FIRMWARE ON THEIR NETWORKS