4 digits 7s display + 74HC595

Rearrange a little

digitalWrite(latchPin, LOW);
shiftOut(dataPin, clockPin, MSBFIRST, digit[j]);
digitalWrite(latchPin, HIGH);
digitalWrite(digits[j], LOW); // turn on the digit
delay(1);
digitalWrite(digits[j], HIGH); // turn off the digit

as LOW turns on the PNPs, and leave them on longer.
1/30/4 = 8.3mS.
So try 4mS.