Yeah, sorry. I don’t think of RAID 0,1,10 as RAID firmware; the 2308s won’t do anything beyond this. That takes a 2208 with its dual-cores. My fault for using incorrect terminology.
You can get the version 18 firmware for your Z840’s onboard 2308 here:
https://support.hp.com/us-en/drivers/selfservice/hp-z840-workstation/6978842
It’s under “Firmware,” and here is the link to the firmware file itself:
https://ftp.hp.com/pub/softpaq/sp68501-69000/sp68620.exe
Hope this gets you back to P18. Once you get this going, you can try and flash generic Broadcom software if you wish. You can get that from Broadcom’s site, under legacy host bus adapters. Just make sure you choose the correct one for the hardware you have, and the functionality you are wanting to achieve. According to this page, it looks like your onboard 2308 is configured similarly to a LSI SAS9217-8i.
Hope this helps.