Use the TPIC6x595 to sink all the cathodes in parallel.
Add P-channel MOSFETs to turn current on/off to the anodes of the digit being driven.
You will need another device in front of the p-channels, another TPICxxxx would work.
Resistor pulls the MOSFET gate high (12V) to turn it off, shift register output pulls the gate low to turn the P-channel on and enable a digit.
So you save on shift registers, but you add "high side" drivers instead, and you cut back brightness to 1/6 of what it could be.
This would be a good mosfet
http://www.digikey.com/product-detail/en/NTD2955-1G/NTD2955-1GOS-ND/1484753 64 cents - plus pullup resistor
while a 100mA/IO pin shift register is less, just 56 cents
https://avnetexpress.avnet.com/store/em/EMController/Counter-Shift-Register/STMicroelectronics/STPIC6D595B1R/_/R-5750380/A-5750380/An-0?action=part&catalogId=500201&langId=-1&storeId=500201&listIndex=-1&page=1&rank=0
All kinds of tradeoffs are possible.