Your vacuum advance set-up results from the need for specific timing requirements under various conditions.
An example is when the engine is cold, the amount of advance allowed by the system will be different than when the engine is warmed up. That's why the vacuum lines are routed through various vacuum temperature switches, etc.
My advice would be to leave the system as-is. If the vacuum advance unit is faulty, replace it and leave the rest of the system intact unless you have a good grasp of the needs of the engine regarding the vacuum advance.
Should you want to experiment, remove and leave open the rearmost (#1 on the diagram you drew) vacuum port on the vacuum advance. Plug the hose.
Connect port #2 to a manifold vacuum source (full time vacuum, even at idle). If the line on it now is a manifold vacuum, leave it on. If it's not, plug it and find a source of manifold vacuum. Use a "T" if necessary.
See how the engine performs and pay attention to any signs of detonation (pinging).
Next, connect port #2 to a ported source and see how that is. Pick the best one if there's a discernible improvement. But I'd be surprised if there's any difference.
Now, that's not to say there's no way to improve what you have.
Sometimes adding initial timing helps performance, sometimes adding total timing helps, or both. But what you do not
want to do is add initial timing w/o verifying the total timing isn't now too high. This is very important because too much total timing can damage the engine with detonation or cause you to have to use premium gas. Tuning it to run on premium is OK, detonation is NOT OK.
Read the section on timing here
and see if it makes sense to you. If you grasp it, you might want to use a timing tape and timing light (or a dial back timing light) to plot the way the advance curve is now, and see if adding some initial or total timing helps, or bringing in the mechanical advance sooner helps. This is done by using lighter springs in the advance mechanism.
BTW, the part marked as a filter might be an intake air temp vacuum switch.