Driving LCD effectively

You can (if your LCD support it) use 4bit. That will leave you using 4 + 3 ? And this is less than 8 so you could implement using a 595 shift register http://arduino.cc/en/Tutorial/ShiftOut using 3 outs.
[if sum is greater than 8, just add a 595]

It will cost some programspace, to implement the logic, but it can be done I think.