Multiple software serial ports doesn't work

[omrimix]

I am using Arduino Uno with 4 scales connected with an RS232 cable. I want to read their data as fast as I can, hopefully without a blocking while loop. I am getting good reads for about ~20s each time, then one of the serial prints garbage, sometimes goes ok again etc. This is my code:

#include <SoftwareSerial.h>

#define SCALE_NUM 4

int rx[4] = {8, 9, 10, 11};
int tx[4] = {6,  7, 4,  2};

SoftwareSerial mySerial1 = SoftwareSerial(rx[0], tx[0]);
SoftwareSerial mySerial2 = SoftwareSerial(rx[1], tx[1]);
SoftwareSerial mySerial3 = SoftwareSerial(rx[2], tx[2]);
SoftwareSerial mySerial4 = SoftwareSerial(rx[3], tx[3]);
SoftwareSerial mySerial[4] = {mySerial1, mySerial2, mySerial3, mySerial4};

int baudRate = 9600;

float weights[4] = { 0 , 0 , 0 , 0 };

void setup() {

  Serial.begin(baudRate);

  for (int i = 0; i < SCALE_NUM; i++){mySerial[i].begin(baudRate);}

  delay(500);

}

void loop() {
        
  readString();
  
  prints();

}

void readString() {
  static String readString = "";
  static int currentPort;

  refreshSerialPorts(currentPort);

  if (mySerial[currentPort].available()) {
    char c = mySerial[currentPort].read();
    readString = readString + c;
    if (c == 'g') {
      //Serial.println(String(currentPort) + " " + String(readString));
      weights[currentPort] = readString.substring(7,14).toFloat();
      weights[currentPort] = weights[currentPort] * 1000.0;
      readString = "";
      currentPort++;
      if (currentPort == SCALE_NUM) {
        currentPort = 0;
      }
    }
  }
}

void refreshSerialPorts(int portNumber) {
  mySerial[portNumber].listen();
}

void prints() {
    static unsigned long lastPrintTime = 0;
    #define PRINT_TIME 500

    if ( millis() - lastPrintTime > PRINT_TIME ) {
      for ( int i = 0 ; i < SCALE_NUM ; i++ ) {
        Serial.print(String(weights[i]) + " ");
      }
      Serial.println();
      Serial.flush();
      lastPrintTime = millis();
    }
}

Picture of the scale:

[horace]

the SoftwareSerial documentation states
If using multiple software serial ports, only one can receive data at a time.
look at using a Arduino Mega which has frour hardware serial ports - one is used for the Serial Monitor so you would have to use SoftwareSerial for the fifth port