Driving a multiplexed segment LCD... How?

Using Arduino Displays
#1

I have a multiplexed segment LCD which has 3 COM pins and requires a frequency= 64Hz, 25% duty, 1/3 bias; see below for pinouts. After looking around, I found this interesting post where the poster drives a similar display but in his case, it has 4 COM pins.

Can anybody help me scale his sketch to just 3 COM pins? Thanks in advance.

The original post is here. This is his sketch.

#include <Streaming.h>
#define cout Serial
#define endl '\n'
const int BP1=7, BP2=9, BP3=8, BP4=10; //backplanes
int S1=11, S2=6, S3=12; //segment outputs.  S1 is always blanked, S2&3 are driven

void setup()
{
  Serial.begin(19200);
  cout <<"Hello from the clock LCD test mule \n";
  pinMode(S1,OUTPUT); pinMode(S2,OUTPUT);pinMode(S3,OUTPUT); //segments are live
}

void loop(){
  int displaydigit= (millis()/1000)%11; //test pattern cycles from 0 to 10
  drivelcd(displaydigit);
}


void drivelcd(int digit){ //drive the LCD to display a digit
  //each of the LCD backplanes is cycled low then high for 4ms while the others are held at a middle-voltage
  //the segments are lit by setting them opposite to the active backplane
  //each bit in the digit segment table below defines the state of a segment for a particular backplane for that digit 
  //the segment 2 bits are first then the segment 3 bits
  //e.g. for a 0(the 1st element) segment 2 is on for backplanes 2 and 4 (0101) and segment 3 is on for all of them(1111)
  const unsigned char dst[]={0b01011111,0b00000110,0b00111101,0b00101111,0b01100110,0b01101011,0b01111011,0b00001110,0b01111111,0b01101110,0b01111110}; //digits 0-A
  static int stateprev=8; //tells us when we change states
  int statenow=(millis()/4)&0x07; //cycles from 0-7 changing every 4 ms
  if (statenow!=stateprev){ //if the state has changed
    //reset backplane pins to input and activate the pull-up resistors
    pinMode(BP1,INPUT); pinMode(BP2,INPUT);  pinMode(BP3,INPUT);pinMode(BP4,INPUT); 
    digitalWrite(BP1,HIGH);digitalWrite(BP2,HIGH);digitalWrite(BP3,HIGH);digitalWrite(BP4,HIGH);
    switch (statenow) {
      case 0:
        pinMode(BP1,OUTPUT); digitalWrite(BP1,LOW); //activate backplane 1 for 1st half of its cycle
        digitalWrite(S1,LOW); //ensure segment 1 stays blank
        digitalWrite(S2,(dst[digit]&0x80)>>7); //activate segment 2 if needed
        digitalWrite(S3,(dst[digit]&0x08)>>3); //activate segment 3 if needed
        break;
      case 1:
        pinMode(BP1,OUTPUT); digitalWrite(BP1,HIGH); //set BP1 2nd half of its cycle
        digitalWrite(S1,HIGH); //ensure segment 1 stays blank
        digitalWrite(S2,!digitalRead(S2)); //toggle segment 2
        digitalWrite(S3,!digitalRead(S3)); //toggle segment 3
        break;
      case 2:
        pinMode(BP2,OUTPUT); digitalWrite(BP2,LOW); //set BP2 1st half of its cycle
        digitalWrite(S1,LOW); //ensure segment 1 stays blank
        digitalWrite(S2,(dst[digit]&0x40)>>6); //activate segment 2 if needed
        digitalWrite(S3,(dst[digit]&0x04)>>2); //activate segment 3 if needed
        break;
      case 3:
        pinMode(BP2,OUTPUT); digitalWrite(BP2,HIGH); //set BP2 2nd half of its cycle
        digitalWrite(S1,HIGH); //ensure segment 1 stays blank
        digitalWrite(S2,!digitalRead(S2)); //toggle segment 2
        digitalWrite(S3,!digitalRead(S3)); //toggle segment 3
        break;
      case 4:
        pinMode(BP3,OUTPUT); digitalWrite(BP3,LOW); //set BP3 1st half of its cycle
        digitalWrite(S1,LOW); //ensure segment 1 stays blank
        digitalWrite(S2,(dst[digit]&0x20)>>5); //activate segment 2 if needed
        digitalWrite(S3,(dst[digit]&0x02)>>1); //activate segment 3 if needed
        break;
      case 5:
        pinMode(BP3,OUTPUT); digitalWrite(BP3,HIGH); //set BP3 2nd half of its cycle
        digitalWrite(S1,HIGH); //ensure segment 1 stays blank
        digitalWrite(S2,!digitalRead(S2)); //toggle segment 2
        digitalWrite(S3,!digitalRead(S3)); //toggle segment 3
        break;
      case 6:
        pinMode(BP4,OUTPUT); digitalWrite(BP4,LOW); //set BP4 1st half of its cycle
        digitalWrite(S1,LOW); //ensure segment 1 stays blank
        digitalWrite(S2,(dst[digit]&0x10)>>4); //activate segment 2 if needed
        digitalWrite(S3,(dst[digit]&0x01)>>0); //activate segment 3 if needed
        break;
      case 7:
        pinMode(BP4,OUTPUT); digitalWrite(BP4,HIGH); //set BP4 2nd half of its cycle
        digitalWrite(S1,HIGH); //ensure segment 1 stays blank
        digitalWrite(S2,!digitalRead(S2)); //toggle segment 2
        digitalWrite(S3,!digitalRead(S3)); //toggle segment 3
    }
  stateprev=statenow;
  }
}
#2