I understand that you are unable to find the micro-code for the processor you currently have.
Upon review of the model you provided I was able to determine that this unit is what is called "Tray" processor, which are processors that are sold to the different OEM (Original Equipment Manufacturers) like Dell, HP, etc and the warranty and firmware or micro-codes are managed by them.
After checking our download center you are completely right, the unit has no firmware or micro-code available so in this case what I could recommend you to do is to either contact the manufacturer of the system in question or else the motherboard manufacturer in order to find mentioned micro-code.
"it's basically the same as the Xeon E5 2699 v4, which does have the latest microcode update"
I see that the 2699 v4 does NOT have the latest microcode update included in the March 12 tarball.
According to the document here https://newsroom.intel.com/wp-content/uploads/sites/11/2018/04/microcode-update-guidance.pdf , the Broadwells which include 2699 v4, are cpuid 406F1 and the *production* released microcode version for it is B000002A . But if you look in the released March 12 u-code tarball , you see the stale version B0000021 in there:
intel-ucode$ od -hx 06-4f-01 |head
0000000 0001 0000 0021 0b00 2017 0301 06f1 0004
0001 0000 0021 0b00 2017 0301 06f1 0004
What gives, Intel? Please don't give the canned response of "see your motherboard vendor for the latest bios upgrade".