Not much difference on power use for the series connected versions. Line operated power supply to battery brings up more questions.
How long does display need to operate at a time?
Alk. or rechargeable? Go with re chg., flatter discharge V.

How bright do LED need to be, a small drop in current might not be noticeable.
My suggestion, use 8 AA's ' use 2N3904 as common emitter drivers [ emitters grounded ], or IC equivalent . @ 2600 mAh a drain of 320 mA about 8 hours.
For longer times try SLA 12V battery.

Ignore use of 74AC02, forgot about other 3 groups.

 

I'll be using a 12V 9800mAh battery, probably in parallel with another, since this circuit is just the tip of a large iceberg of a big project.

My overarching concerns are prioritized thusly:

1) Supply is 12V
2) Stable performance
3) Limit current draw where possible
4) LED brightness

There are going to be micro-controllers involved in the larger project, so I could multiplex and all that, but I'm trying to keep non-dynamic circuits as isolated as I can; basically, apply power and they work. I may run a timing pulse from an MCU into the 4017 just for the ability to change the frequency with software, but that's not important at the moment.

 

Quick update:

I got the parts for this circuit and am in the process of bread boarding it (which I hate). I got my 4047 working, and my 4017 works, but I'm having issues with the 4001s. I tested them individually to make sure I was connecting them correctly, but it raised a question. How quickly are these gates supposed to switch? They seem to be switching correctly (I'm using an LED to see the state change), but there's a lag or so where the LED seems to go bright-dim-off instead of bright-off. I'm not testing with a decoupling cap, but would that really affect it? I can't find anything int he datasheet that states how quickly it should switch, but I would imagine it should be faster than my eye can pick up on.

 

Which schematic are you using?
Are you using a common colector driver for your test LED?
Switching times should be less than a μS.