@iamtherealJayy I on a computer with no sound but I will watch the video later and take my best guess as to whether or not it's been camed.
So the metering rods go into the main jets, effectively making the main jets smaller for cruise operation, as you step down on the gas vacuum is reduced, and the springs in the metering rods over come the vacuum and the metering rods go up allowing more fuel in. How much more fuel is the effect of the size of the metering rod, the tapper of the metering rod and the strength of the spring. Since you can remove the metering rod with the carb top still on the carb it is possible, with the right tools to be able to unscrew and remove the main jets with the top of the carburetor still in place. Remember that the main jets are brass so it's not like they can be pulled out of the bottom of the bowl though the metering rod hole with a magnet. I think guys pull the carb top to change the main jets. Secondary jets back by the secondaries in the bowl so for those it's a requirement to pull the top off the carb. Spring colors for the metering rods will be obvious colors.
I think your mixing up you timing terminology.
Initial timing (sometimes called base timing) is the timing without vacuum or mechanical advance and is what you normally check and set at idle.
Vacuum advance is the amount of advance given by the vacuum can on the side of the distributor.
Mechanical timing is the amount of timing given by the mechanical advance unit inside the distributor, which is controlled by the weights and springs under the rotor.
Total timing is all of that added up.
It would be best to set the initial timing to whatever is listed on the sticker under the hood, if the sticker is gone 8 - 10 is safe and what you should shoot for, especially given that the mark you make no matter how careful you make it is unlikely to be as accurate as a timing tab. Don't worry to much about checking total timing, because it's a stock motor, the distributor is very likely stock, so we wouldn't be looking at total timing for the purposes of tuning, it would just be to verify the mechanical and vacuum advance is working. After you have the initial timing set with the vacuum can disconnected, just give the engine a good rev to see that the mark moves, at least in doing that you'd know it's functional. You have said the inside of the distributor looks good, so as long as you can get the initial timing close I think that would be fine. Part of that is though our discussions of your symptoms this really does seem like a carburetor issue you are fighting, so I'm really not concerned about an advance issue with the distributor, but you do need to set initial.
Let me know if that make sense.