If the HDD swap doesn't work for you, try searching for FactoryServiceMode_Lv2diag_RSOD.rar. You should find the archive (or file) and instructions on how to use it. This is said to be the best and safest way to fix a RSOD PS3 (as far as I know), but it didn't work for me. I ended up using 355-NOTHEROS-RSOD.PUP and rsodfix.gnpdrm.pkg, which I read should not be used because there is a high chance of perma-bricking your console. Read up on that and if you do decide to try it, do it as a last resort.
This is what I did.
1. Installed 355-NOTHEROS-RSOD.PUP from the RECOVERY MENU.
2. Installed rsodfix.gnpdrm.pkg from XMB.
3. Ran rsodfix. (the instructions say to reboot the PS3 after this but I didn't)
4. Installed Rogero CFW from XMB.
I didn't think it would work, but it did. The RSOD reappeared two weeks later so I had to repeat the process, but it hasn't happened since.
You should be able to toggle FSM with an E3 Card Reader. I bought one just for that same reason, although I have a phat PS3 so I don't know if there are any compatibility issues with the slim.