Properly install Roxul mineral wool batts in a mostly-drywalled stud bay by pushing them up from below

If you shift more airflow upstairs, it's likely it will become noisy. Do not restrict anything unless detailed duct size analysis indicate it is indeed oversized. Insulating ducts will reduce resonant noise, and slightly reduce carried noise such as combustion noise, but it will not stop the whistling and air flow noise at the grille. If you do get insulated ducts, they need to be upsized to make up for the insulation thickness.

To reduce whistling and air flow noise right at the grille, you need a less restrictive grille. Sometimes just a different grille of a different configuration will stop whistling, but not air flow noise. If a less restrictive grille is not possible, the only other solution is to increase the size or add another inlet so there is less demand on the one by the bedrooms.

All right, I found a manual for a nearly-identical unit and cross-referenced what it says with applicable sections of the 2012 International Fuel Gas Code. Now I feel like I have a much better idea of what's going on.

The huge duct is supplying input air for combustion and dilution through the attic, which is code-approved and is sized correctly. There's a hole in the ceiling of the furnace room that I didn't even notice; it's for the output air. It all corresponds perfectly to this illustration in the code:

The alternative is to get the air partially or wholly from inside the conditioned space as long as the building envelope's tightness isn't 0.4 air changes per hour at 50 pascals of pressure or better, which my house most certainly is not (that's Passivehaus-level!). In this case, I would need 50 cubic feet of interior airspace per 1000 BTUs of all interior gas-fired appliances. The furnace draws 125k (waaaay too high), and the gas range is capable of drawing 54k when the oven and all the burners are firing. So the worst-case scenario is that I need 8950 cubic feet (or 1118 square feet) of interior space when all these appliances are in use. I don't have that; the whole interior is only 1100 square feet, and I can't even count bedrooms and bathrooms that have doors, reducing the amount of square footage I can use for combustion air purposes to 650, or 5200 cubic feet, or a maximum of 104,000 BTUs worth of gas drawn by interior gas appliances. Even downsizing the furnace, I will still likely exceed that, and the deficit will get worse as I air-seal the building envelope.

So I have to keep the existing setup, which is all kosher with the code and perfectly safe. And I'll never get carbon monoxide poisoning. So that's good.

The question becomes how to offset the energy penalty of having two huge penetrations into the conditioned space where outside air can flow. I'm thinking that my best option is going to be separating the furnace closet from the rest of the house as much as I can. There are huge holes and thermal bypasses which I'll be sealing up, and if possible, I'm going to add insulation to the stud bays separating the furnace closet from the rest of the house. In essence, I'll turn it into a mini-unconditioned-space within the conditioned space.