Driving 14 or 16 segment LEDs

Check maxim-ic.com.
They have 14-segment drivers, might need 1 per chip. Or maybe will have 1 that does 2 chips.
But really, using 2 shift registers and a ULN2003 or TPIC6B595 is not that hard.
Write a blink-without-delay piece of code: at the top of void loop, you check for 500uS, or 1-2 mS, passing, pull the next digit of data from an array and write it out and turn on the next cathode driver for common cathode displays , or anode driver such as UDN2981 if you have common anode displays.
The rest of the time your program does whatever it does.