There are many variants of Hall sensors around,
you may try to find out what make and type is used, and search for a Datasheet.
Some sensors may be just the Hall sensing element, and deliver a low level analog signal,
This will need analog comparator (in microcontroller) and maybe also a operation amplifier.
Some sensors have amplification and detection circuits integrated, and deliver a digital signal as output.
Output may be open collector, alias open drain circuit, and require a pull-up resistor somewhere.
You may try redoing wiring to existing sensors, with twisted pair wiring separately for each sensor.
Signal & Vss(aka. ground) in a twisted pair for each sensor,
and Vss and Vdd in another pair with decoupling 0.1 uF between Vss and Vdd at the sensor end.
Or screened wiring separately for each sensor.
If you have access to a oscilloscope, study the signal quality reaching the controller.
If there are ringing and reflections,
a series resistor between 20 and 100 Ohm, in series in the signal line, may help.
It is possible to detect the state of a three phase BLCD or PMSM motor without using hall sensors in the motor.
It is done by sensing voltage on each motor wire in the time drive to the respective winding connection is switched off. Also current sensing may be involved.
Microchip have made many Application Notes on: Sensorless Motor Control...
They do this to promote use and sale of dsPIC microcontrollers with builtin ADC and OP-amps and analog comparators, and motor control PWM peripherals.
It is a big subject with some learning curve.