OK guys, I've got some good news:
You can set the BMS password using the JBDTools Windows app (the Chinese version, downloaded from Overkill Solar website). That is if you have the UART to USB converter for the JBD:
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Overkill also has their own version which will allow to clear the password, but not set it.
For some reason, the Chinese version showed me all question marks instead of English on the "Other options" tab, but from Overkill's attached picture (came in the zip file) I was able to understand what textbox to enter the password in, and what button to press (both marked in red circles):
From overkill:
View attachment 82550
From me running the app:
View attachment 82551
Please note you need to enter a 6 digit number!
I was successful, and when I disconnected the Uart adapter and connected the Bluetooth dongle, it asked me for a password when trying to connect to the BMS using the Android app.
So there you go... it's possible!
P.S. Do this at your own risk!
I was successful with a 4S 150A JBD BMS, but it might not work for you...