The installation instructions document which RPi are compatible.
BT transmission from a polycarbonate/Styrofoam shell is going to be inherently different from a big chunk of metal that is imbedded in a EM field of its own creation. Comparing the two is the proverbial apples to oranges situation. Expectations of one based on the other is not realistic.
The BMV-712 has improved BT range because it's NOT in the shunt. It's in the display outside of the shunt's EM field.
Either you start over, or you finish the exercise. The correct RPi can be had for < $150, and in this market, you can probably recoup some of the cost of your 400.
I'm not against throwing more money at it if it will bring a solution. But, if I buy a couple more components and still have to walk out in the snow to get the battery status by looking at an LCD display, vs standing there looking at my android phone app via Bluetooth, I am still standing out in the snow.
I have literally thousands of dollars of equipment stored in boxes that were part of design projects that were never implemented. I spent my working career as a electronics engineer, working in R&D, doing design and implement, and as a senior software development engineer. I wrote software to control the machines and report data readings in human readable formats. Also, during that time I spent nearly 30 years in the IT profession. From it infancy to present.
The big difference is that now, being retired, I do not have a fortune 500 company supplying me with whatever I want/need to think up, design, troubleshoot, implement, and support, the gizmos that make things, work and communicate with other gizmos, and of course, humans. I have no sponsors, no freebies, and certainly no way to recover my costs from items that just don't fit the project or perform as expected. R&D is expensive because not all stuff works as advertised or designed. And, some devices do not play well with others.
So, that is my reason for asking. I am gleaning from the research and development (R&D) of others so I can obtain the results I need with out putting more in boxes for my descendants to get rid of when I am gone.
I hope some if this makes sense.
Ken