I need to look at the datasheets again, but anyway I was thinking of a high e.g.
https://www.google.com/url?sa=t&rct...=utFr6btCnp4FmvCafpetXw&bvm=bv.91427555,d.cWc and low side driver, but you may have to convert the output to a logic level.
The 2803 adds another 1.2 volts. The internal high side driver probably has a voltage drop too. You could simulate the worst case by using 3 diodes in series with your string.
You seem to be on the hairy edge of everything.
I'm thinking, probably in terms of a multiplexed display outside of the normal limits where you would need a high side driver for the segments and a low side driver for the digits.
In that case, you would have to account for a possible voltage drop for the segment driver and the voltage drop for the digit driver. If you use a darlington like the ULN parts, that would be another 1.2 V to account for.
If you break the segments into two, then you also have 2x the current to deal with.
Can you do the following. Use a 12 V supply on one segment with 3 diodes like the 1n4001 in series and see if it works. You might have to change the series resistor.
Measure the voltage across the series resistor and translate that to a current so, we can see if everything is in range. For fun, you can also measure the voltage drop across each LED to get an idea of the maximum and average drop.
The design may be too close to the limits. If my memory serves me, so parts have a 20 mA limit and some have 40.
Meanwhile I'll look at the datasheets.