My guess is that your house is fairly well insulated and has decent AC. Our place has horrible insulation, and surprisingly adequate AC (but REALLY old, 1991, and inefficient). Any source of heat (or cold in the winter) is noticeable for us.
Yeah, we'd wondered about and talked about that. And 2 of the spots upstairs have doors. One is boards connected but with 1/8" or larger gaps between them. May as well be no door, and all of the heat from the attic pours in. I've currently got the gaps taped with aluminum tape, just to kill the free air flow.

Several of the closets had home made doors, 3/4 ply, some with TnG bead board applied as doors. They weighed a TON.

Old houses and that was how it was done back then. When materials were available, they used it unless its a custom high end home where materials were pocket were deep. I torn apart homes that were built in the early teens and they were a huge improvement by 1930. Standard building code got much better and just the standard itself were much better.

Frame the opening, header off all openings, build simple plywood doors with 2x surround. Buy a 4x8 sheet of 1½" rigid insulation which will insulate all four doors.

If you're dealing with drywall rather than plaster, why does it matter? Frame the opening, patch the opening and mud.

BTW ya ought to see this new system I'm installing in my house. I bought a Bryant Evolution Extreme heat pump, Bryant Evolution modulating 98% efficient furnace and an Evolution system controller. The tech is just ridiculous! I did a load calc on my house then sized based on what the tech specs called for. The gas furnace and heat pump can vary output based on the load sensed by the thermostat. Based on the load calc, I can run the heat pump down into the teens before I hit the balance point. I plan to add Bryant zone dampers next year to zone the house. It's expensive but should be a considerable energy savings vs the system I installed almost 30 years ago.

Fortunately, no buried wood. The owner that bought the house around 1990/91 updated a lot of stuff (added central HVAC, replaced knob and tube with modern electrical, etc...). I'm assuming that person (or someone since then) has had the home leveled. All of the piers are cement, and all are on top of cement pads.

Our ground here is clay. We can go from saturated so that the yard gives under you if you walk through it, to so dry that there are cracks anywhere from 1-2" wide.

I am also going to have to create a hatch up into the attic at the peak as well. I don't need or have space for a ladder. I installed one in the garage of our old home.

The plan is something similar to that. I think I have headers in place in all of the openings already. The only rigid available easily around here is 3/4". But I do have a bunch of 3/4" so I'll stack a couple/few of sheets of 3/4".

I hate doing drywall, LOL!

The new HVAC sounds awesome! I'd love to have something like that at my place.

I get hating drywall work. But ultimately it might be cleaner, easier, and a better seal if you can buy a pre made door system and make the opening to fit. Frame the opening... sling a little board, use 90 minute easy sand compound so you can hit two or three coats quickly, sand, paint done.. Easy peasy. Probably have more time messing around trying to build and insulate the door.

I've been waiting on the weather to turn more fall like where I won't really need the A/C during the day. Once I see those temps in the forecast, I'm gonna tear out my old system and install the new. Shouldn't take me more than two days out and in. Btw, the dealer cost for the equipment, not pretty. I wouldn't want to pay the markup price. I'd bet a normal dealer would charge 15K or more for just the furnace, heat pump, evaporator coil, thermostat and for me a propane conversion. Then put installation on top of that. The price of technology ain't cheap.