Okay so just an update for anyone curious, I was able to follow these instructions which allowed me to update the firmware on the 9201-16e, and then repeated the process for the 9300-8i so they are both up to date. But then for some reason I wasn't able to boot and get a GUI. Couldn't spot any errors in the log, so I tried booting Unraid in safe mode and hurrah. Was able to assign my disks back to their original assignments using a new config, and tested that it was all working. Seemed fine so far. So I booted back into non-safe mode and it ended up booting fine, no problems. Now have been able to assign the four new drives to the array and all seems to be working well.
Something strange though - when the system boots, and I get the BIOS screens for the HBA's, it says to press Ctrl+C to enter the config utility, which I wanted to do so I could disable the HBA's as boot devices. However the system just doesn't seem to respond to the Ctrl+C keypress and I can't for the life of me get into the configuration. Not the end of the world, but a bit frustrating. The main thing is that the system is now booting and recognizing all drives in both HBA's. Thanks very much for your help @JorgeB.