I tested the counter and I am getting a signal at both outputs with no changes made to the circuit. I know the circuit is not operating as you want it to, but right now I can't isolate what is causing the problem.
In such a situation, I usually Isolate one subcircuit at a time, get it working correctly and then hook it to the second one and so forth. You may have to do this in order to find out where it deviates from what you expect as an output.
This is the only thing I can suggest at the moment. I will continue looking into this, but with so many nested subcircuits it may take a while. I cannot guarantee finding a solution, but I will try.
I am not certain if this was intentional, but when I run the simulation I get the numbers changing, but also the displays get switched. Instead of displaying a 4 digit number at the same time I get one display showing one number and then it will switch to another display.
I am thinking it has to do with the last multiplexer. By switching the outputs from one display to another it takes away the voltage to the first display and therefore switches it off.
Here are my conclusions. Your circuit on my machine is working. The thing that is not working correctly (my opinion) is the fact that when you do the switching in the last multiplexer it blanks one display and then lights the next one. If you are wanting all the diplays to be active at the same time you are going to have to get into the last multiplexer and find a way to do that.
My previous post is accurate. It cylces the displays instead of having them all on at the same time. I am not sure this was intended, but if it was then your circuit is working fine.
I hope I have helped some.
If everything is working as I suspect, then I have to say that this is a brilliant circuit and design.
I would like to bring to your attention about the X2 Subcircuit has your test setup still inside it. Before you finalize this you might consider deleteing these testing components. Also the 7 segment display inside this subcircuit is the wrong type. It should be a common cathode. I would also suggest putting a 50 ohm resistor in line with it to ground like the other displays in order to eliminate an error message popping up.
I am glad you got it working. I thought as much about the cycling displays after analyzing it more carefully. According to what I see now though it is cycling way faster than every thirty seconds. You may have it this way for testing purposes (which is what I would do instead of waiting forever for the simulator time to reach 30 sec.). Reguardless, I am happy you are happy with it.
Congratulations on a wonderful design.