[jan-jaap]

So I was at the Broadcom site for something else and dug around for the SAS3442X-R as well.

I can't find a product support page anymore (it's retired), but it's possible to find individual download links:

[Unknown filetype] SAS3442XR_P20_Supports_SAS_1-5G_3G_6G_and_SATA_1-5G_3G_HDD

and

[Unknown filetype] SAS3442XR_P20_Supports_SAS_1-5G_3G_6G_and_SATA_3G_6G_HDD

So, not only does newer firmware exist, it seems you need to choose a firmware depending on your (SATA) disks. I downloaded the firmware and can confirm that (1) the firmware inside both zip files is different and (2) there's firmware inside for B0 and B1 silicon, but not A0.

Finally: I don't know what firmware the SAS3442X-R in my O350 has, but I have no desire to flash it. Maybe one day if I feel like striping a couple of SATA3 SSDs. 

Edit: this is only for the 3442X-R, there are other downloads for the 3800X etc. Search and you'll find.