not understanding 7 segment multiplexing

CrossRoads:
Yes, can mulitplex the shift register across the digits. Still need to switch the 12V on/off to the common cathode of the digits tho.

I' d personally ditch that board you have, get an "island of holes" board, futurlec.com has plenty of options, cut down to size you need, and have the WHOLE board available for use. You're backed into a corner with that thing.
http://www.futurlec.com/ProtoBoards.shtml $1.50

Those do me no good. I need something small to fit in a 5x2.5x2 enclosure. Eventually I will transfer it to PCB and fit it in a 4x2x1 enclosure (the thinner the better).

So if I multiplex source on the register and sink on the darlington, that's a DIP20, DIP18, a STDP switch, and 5 pins for the voltage regulators. Leaves 3 columns empty I think. Sounds good.

Everything stays self contained on that board, regulators go off-board, and an RJ45 breakout (or two) and the mini.

Wait- aren't these low side drivers? I need high side. For something so simple, I don't understand why they don't exist (particularly in DIP form). Seems to me there's no difference between the chip you posted and a darlington, other than being SPI rather than direct drive.

Can I simply use 4 Logic Level P-FET's, one per digit, rather than driving a PNP with an NPN?