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:
![enter image description here](https://i.stack.imgur.com/7g5PM.jpg)
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.
Your front door probably currently opens inward. If you try to just flip the door such that you so not have to change around the hardware on the door (old outside becomes inside and old inside becomes outside) then the door would be oriented to as to open outwards. The door's frame is likely not at all compatible with this.
If the hardware on the door can truly be flipped such that the hinges can be swapped to swing from the other edge and the latch and deadbolt can be flipped side for side then you have a good start. However it is not just the door that you have to look at. There is also the door jamb that would require some significant work. The hinge cutouts need to move to the opposite side as well as the latch and deadbolt holes and strike plates. This consideration is probably best done by just replacing the whole door jamb as trying to patch the old hinge cutouts and latch holes can always look like a patch job.
Best Answer
We have the same arrangement in our 1970 house with slab on grade foundation--both water heater and furnace natural gas fired in a utility closet centrally located on the living floor. All of the houses in our Fox and Jacobs 200 house tract neighborhood are built that way.
These gas fired heaters get their combustion air from inside the closet which is open to the the attic via wire mesh in the ceiling. The double doors to the living space are standard hollow core doors, no vents, and seal fairly well.
The conditioned air is pulled into the furnace air handler through a plenum below.
In your case is there a wire mesh over an opening into the attic? Is the attic vented (soffitt and ridge)? Or do your water heater and furnace get their combustion air from outside via roof or soffitt vents?
It would be highly unusual for the WH and furnace to be getting their combustion air from the living space, but if they did then you would need a grill in the door, otherwise no.
But find out what is code in your jurisdiction.
EDIT Another possibility: Where does the air flow into the air handler enter the closet? My parents had a small, nicely built retirement home in which the air entered the air handler through a vent in the door. The door when shut sealed against the inlet to the air handler. If you have this arrangement, the door must be vented. In my house the air enters under the door through vents into a plenum and then goes up through the filter, the fan, the furnace and the a/c evaporator