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Hi Oskar,

if you want connect 8 individual 1 digit displays you have to connect all = 8 A-segments together. Also the B-segments etc. So you have 8 wires for all segments include the DP.
These 8 wires are to connect to the corresponding pins on the MAX-board.
Same with the 8 individual common cathodes. The have to be connected to the corresponding pins for the cathodes. Digit 1 to cathode of digit 1 of the MAX-board, digit 2 to cathode of digit 2 of the MAX-board etc .

Here you have 2 pictures which should help you to connect both ways:

Your "both" are right.

Please appology for Stephan. He is a professional electronic freak and do this stuff in job for all of his lifetime. So he mostly tell you the easy and most logic result....
BUT... Your idea was correct, too (whatever it is much more difficult as needed)

In the Picture of Stephan above you see.... the MaxTubes are Designed for 2x4 Diggit Displays. If you pull OFF the Diggits you have on each side 12 Pins !
12 Pins you already understand after our last guiding yesterday.... It means for a 4 Diggit Display : 8 Segment Lines and 4 Cathodes = 8+4=12 Pins !

Look again on the Pictures.... so you see.... The Left Connector include SEG-A until SEG-G and DP ... AND Cathode for DIG1 - DIG 4
The Right one have again this 8 Segment Lines And Again Cathodes for DIG 1-4
Here this is a bit confusing. They write again DIG1 -DIG4 but basicly this are DIG 5,6,7,8 .

So you can see... The SEGMENT Lines are simply shared..... The SEG-A Pin on Left block is the same wire like the SEG-A Pin on right side. This is just split by the manifactur to allow a easy connecting of this 2x4 Blocks .

RESULT:
If you wire 8 Single Diggits on ONE Max you not need to Split the SEG Lines of 4 Diggits to the Left Connector and 4 Diggits to the Right.
For SEG Lines you can use simply ONE Side......
But IMPORTANT !!!! The Cathodes of each Digit must be used SINGLE and correct.... Diggit 1-4 is set on LEFT Connector ... Diggit 5-8 on Right !

Last Note: Not share Segement Lines over multiple Max Tubes.... Each Max7219 is a individual system (whatever you use a chain) NEVER combine a Segment Line of different Max Tubes !

Wow, thank you guys for making this comprehensive.
So if I, for example, would like to build the Electrical panel on the 737. It requires 12 digits in total.
Then I could make the first 8 digits on the first Max7219 board, then daisychain a second board and connect the remaining 4 digits to that one?

This seems like a golden opportunity to use a prototype board instead of connecting a million or so cables to connect the segment pins, or am I in the wrong here?

Basicly Yes....Now you understand the logic.

Next Step is to think about the most comfortable and usefull solution.

At First... If you use Single Diggits you must wire 96 single wires. This is a lot of work. Maby you should think about using 2 diggit and 3 Diggit Blocks if you like. Then you reduce wirework a bit......
Perfect way will be a PCB .... so you just solder the Single Diggits on it and all the "lines" are on the PCB ..... Finaly you just got 2 Connectors with 14 Pins each to connect to the Max Tubes ( Or if you are good in electronics you can also include the Max Chips on this PCB..... but here you should be verry advanced. )

About splitting....

Rule 1: You can not show a config over multiple Max tubes.... So if Possible find a logic that every used Config is set to ONE Max.... So try to net get in situations you like to show for example 2 Diggits on Max1 and another 3rd diggit on Max 2...... This is possible but difficult and unpracticable.

Rule 2: If you use the MaxTubes with removeable Diggits try to use the Pins in a comfortable way.....
In your example you need 5 Blocks ( 3x2 Diggits 2x3 Diggits. 9
So i would split 6 diggits (3x2) on Max 1 .... and 6 Diggits (2x3) on Max 2
On Max 2 you can use 1x3 on the left Port.... and 1x3 on the Right Port.
On Max 1 you can use 1x2 on Left Port and you only need to combine now 2x2 on the right port.

But sure.... this is just a idea from myself..... You can do it in lots of other ways.

Last Note:
I not know your hardware Panel.... Do you have Space Left and right of the displays ??
If yes then you can think about using simply 3 Diggit Blocks for all 5 Display Parts.... This make it much more easy to wire. .. all Displays look same.
If Size of Displays is ok and you have enogh space on the sides you "maby" can also use the Original 4 Diggit Displays from the Max Tubes.... In That case you just need a 5.th Diggit block and if you not like to combine the cables you should work with 3 Max Tubes instead of 2 !

Summary... FIRST Think about your project.... SECOND make a Plan .... And always think what is the most comfortable way .... A Max costs only 2-3 $ If its more easy to bild it with 1 additional Max tube then do it.... 5 Hours of soldering and wire work costs more then 3 $ for a Maxtube!

I received both the boards and the 0,56" inch digits now, and the 0,56" are gigantic. The ones delivered with the boards obviously are 0,36". It will work anyway though, I suppose.

My next issue is that the sockets in the boards have connectors with very small holes (corresponding to the thin pins on the 7 segments). How do I connect these externally? Dupont cable pins are too wide to fit.

a secure connection is e.g. made by soldering.

DuPont cables are very well suited for test setups, for the final connection in a panel at least one side should be soldered, the other side with twisted sockets to be plugged.

Sorry Stephan, I don't understand what you mean.
If I need to desolder the socket on the board, I could as well have used my Max7219 with fixed 7 segments?

You say that the jacks in the board connectors have small holes and the DuPont cables would not fit.

Therefore, I thought that you should solder these compounds. On the other side of the cable, you should take twisted IC sockets (you can disconnect in the middle).
These ensure a very good contact and ensure a stable connection.

Stephan means for removing a part, only ONE Side must be removeable....
In your case i would say the maxtube (with the chip) will not get broke in the future ( Only by a High Power issue but that not happend normaly)
So the "critical" Part here is only the Diggit itself.

In that case you can Solder your wires on the MaxChip. ( No removeable connection is needed here) and you maka a Dupont Connector on the Diggit side.
So you can Remove the diggits if needed.... Just the Wire on max is soldered.

About your Question:

Dupont Crimp Contacts are "Standard" size.... there exist also the kind "Precession" ( I hope this is the correct name in english) . These are smaller. the Conntector bridges on the empty Max Tube are in this kind.... And the Pins of the Display are also precession and smaller like standard Dupont Pins

Solution:
1. Solder the Max Side like Stephan said.
2, Buy special "precession" Contacts ( Male/ Female) to build connectors that hit on the Max Tubes perfect.
3, Build your connector DIY.... Use silverwire ( hard metal wires in thiknes you need ) and solder it on your used wires. You can also use "Empty Connector boxes" to fix these wires together and build a connector you can simply set on the bridge of Max tube,

Summary... Lots of possible ways.... But just think if you realy need a removeable connection....
Its lots pof work to build it removeable.... If realy one device get broke after 10 Years its less work to resolder this one part instead of build connectors now for all stuff !