Many thanks again for the help on this. Somewhat improbably, I now have a 
working LED-based prototype on the breadboard - it includes the modes of 
the original and a few new ones too. I have multiplexed it for now - to 
save space and bits at least - I started out the hard way but then 
discovered the timer interrupt of the Arduino chip which makes it much 
easier. But my display is fairly well abstracted from the rest of the code 
so if it turns out I want to direct drive, it's not rocket science to 
change it.

So my circuit is fairly simple - In each multiplex cycle, the Arduino 
writes out to 3 74HC595 shift registers:

* 1 controls the anodes of the 14 segment displays (just one at a time in 
this case) - these go through 2N3904 transistors, since the total draw of 
one character is more than the register can handle

* The other two control the segments; for now I'm using resistors such that 
the 74HC595 can sink the current so they are connected directly to the 
cathodes.

Now thinking about moving up to the tubes. Very simplistically, I'm seeing 
the eg B7971 as a bigger version of the common-anode LEDs I'm using - just 
requiring a higher voltage and current, so needing to be driven through 
appropriate transistors. I'm sure it can't be *that* simple though - can 
anyone broadly summarise what other things I need to consider?

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