Thanks very much for all the comments.
We're looking at the MIC5891 for the anodes. That's a 595-type shift register, which handles much higher voltage and current. Its outputs are open emitter darlingtons, so I was hoping there would be no need for a ULN2003. And besides, I thought the ULN2003 could only sink - it has a common emitter and open collectors. His displays are common cathode, so we need to source high current into the individual segments. I don't know of a cheap 7-gate darlington array with open emitters.
Then he already has the TPIC6C595 on hand, which would be on the low side, with one input connected to the CC output of each digit. He would need two of them to handle 11 digits.
Is this for a scoreboard or something like that? I really wonder if 60mA/11 digits = 5mA average would be bright enough.
I don't know what it's for, but I have the same question about brightness. But these days LEDs are so efficient that it might work. However, it might be possible to split up the digits into 6 and 5, and drive each half with its own MIC5891. The two TPIC6C595's would still be enough since there are still only 11 digits. That would effectively double the brightness on the same current since each segment would be lit for twice as long. So it would be 60/6 = 10mA average current. But that's still better than 11 MIC5891's at $3 a piece.
What about just making some higher voltage BJT drivers for the LED's ? Just some 2N2222/2N3904/BC547, anything like those would be plenty fast for switching LED's up to the kiloHertz or whatever you would need to be picked up by a camera.
I don't think there is a problem generating the current. The MIC5891 has darlington outputs, which should be good enough. What I was concerned about was switching the current at 10KHz - I don't know what could go wrong doing that - reflections, or spikes, or whatever things professionals know to watch out for, but hobbyists like me don't.
You only need 60Hz per digit, so an 11 digit multiplex is 660Hz, or an interrupt every 1.5ms.
For video, perhaps, but still pictures are the complication. What if the shutter speed is 1/1000 sec? This requirement is the biggest obstacle to this working easily, but he was pretty clear about needing it, and it's why he was planning to make it continuous. I was just hoping there was a better way using multiplexing.
Well, I'm still not clear about whether switching the currents will cause problems. I know that as lines get longer the frequency that can be supported reduces. And presumably the same as currents get bigger. I just don't know at what point that starts to be a practical problem. I mean, 10KHz is not exactly RF.