I am going to take a break for a few weeks from this problem (sometimes you need to walk away and get a fresh start). I have not given up yet, (never give up ), this is a great learning experience.
Yes, all counts.
It's very possible that your thinking is going in circles and maybe even shrinking ones.
You'll find it out afterwards, as how fast you think how simple it finally was.
Your exact motor is still unknown.
If its end has some electronics, other than those feedbacks, you can start thinking those controller outputting pulses differently, after checking how the good controller is operating.
There are practically three ways the controller can order the other end.
First is simple DC voltage, there motor end does necessary modifications for movements, this is also a type where motor movement and its feedback are sort of isolated.
So here controller put out a voltage and read from feedbacks what is actually happening.
Second is where DC voltage is pulsing, there motor has less control of what happens and controller can expect some feedbacks after every pulse.
Third way is where controller is actually a second controller and first controller is inside a motor.
So here the external controller is sort of ordering the internal controller to do its job.
There a pulse can include many things but so can feedback, so different feedbacks can be combined to one signal.
It's also a way where external controller doesn't need any power outputs.
So since your system is clearly outputting power only first and second ways are probable.
Checking the good one will also instantly reveal how the thing actually is.
Keep also in mind that you may have contact problems and initial situations.
Maybe your motor is seeing a low voltage and goes to safe mode.
Feedbacks have four wires, Green is possibly Common, if so then one wire can go out and one come back in.
You can possibly also check how the power pulse does compared to how it should.
If 12V part is shorter than with the good controller you can expect that there is a some sort of a safe mode.
But controller seems to be without any current sensing.
If current sensing is not there the motor can still has it, but there are no dedicated feedback so it must be combined.
Tachometer is most likely all by itself but limit switch wires can have multiple meanings.
There are also two connected relays, assumed operation is so that their states are opposite, that's also how I understand your drawing.
So one relay is putting BAT+ out and other one is connecting BAT- through U11.
So if J5 doesn't have U11 thing the relay is stuck or some connection broken somehow.
That is not electrically bad since it's the same as the other relay or nothing, but then motor obviously can't move.
Chips,
Zilog on low left of the picture seems to be a radio thingy.
Y3 and resistors around U14 indicate it's an MCU, maybe Zilog Z8.
Based on those U7 is probably also Zilog, something slow, maybe Z8 also.
What type is a possible switcher U2?
Some hazy parts.
Is there only one limit switch for two arms, are you connecting both arms through the same connector?
Is third bad board behaving differently than other two bad ones?