Its advisable to run the "FIX_PERMISSIONS" package every time you FTP a game over to the internal drive, apparently 'some' ftp clients change the permissions on the PS3 and can cause games to black screen or have issues when trying to save games.
if you only ftp one game over run the fix once, if you ftp over several game just run the fix once. whether its 1 game or several games you just need to run the fix once.
Not sure if you saw THIS post or if it will help, but it does deal with Heavy Rain so worth a peek perhaps.
Run game from internal hdd 3.55cfw (Game works on usb after all the installing and updating). I had the same problem with heavy rain freezing when i tried to update it online. So how i fixed it was i started the game like normal skiped the online updates and installed the game to my hdd.
Then restarted the ps3 and loaded up the game once agine and when it prompted me to install updates i hit yes and success.
try permission fix from page 4 the file is there to download, this should work for you also you will need to run all games that have any file over 4 gig on internal you can use software to split files over 4 gig to external drive then transfer them onto internal but you can't play games with files over 4 gig from external drive.