Can't update my Macbook firmware
Your question does miss some key details, so this answer makes the following assumptions:


You've correctly identified your current Boot ROM version
Your MBP still has the original Apple SSD installed
You've already tried (directly or indirectly) resetting the NVRAM
You've never installed macOS High Sierra on your MacBook Pro


Essentially, some years back Apple started automatically including firmware updates (if/when required) within macOS updates/upgrades. And, with the move to the APFS file system, firmware updates were required on pre-existing Macs with SSD drives to support macOS High Sierra (and above) as they required APFS to be installed. So, cutting a long story short, you're most likely missing this firmware update. 

Since you've already gone through quite a bit of frustration, your best bet is to go through a total reinstall process. My recommendation would be to do as follows:


Make a full backup of your data using Time Machine (or your preferred backup solution)
Shut down your MBP
Switch on your MBP and immediately press and hold the OptionCommand ⌘R keys *
Let go of the keys once you see either the Apple logo, a spinning globe or a firmware password prompt 
When the macOS Utilities window appears select the Disk Utility option
Proceed to erase your internal drive
Quit Disk Utility
The macOS Utilities window should reappear
Now select the Reinstall macOS option
Proceed to install macOS
Once the installation is complete, migrate your data across


* This specific key combination will install the latest version of macOS compatible with your model Mac, which presently is macOS Mojave.