Could you put an access in the closet instead? Why would it have to be a permanent access if the living room is the only option? Another avenue might be to make an access on the exterior if you have gable ends.

If you have an attached garage, maybe you can access there but keep in mind that all the access openings will need to have a fire rated closure such as a rated door with spring hinges or simply fire code 5/8" sheetrock for a removable lid when in a closet. You can check in with your local building officials for details.

This is our house.

The living room is in the bay window. The second floor bedroom is in the rectangle window above the living room. There is a cold zone between the floors that cools any forced air heat before it reaches the bedroom. When we removed part of the wall in the staircase, a cold breeze blew between the first and second floor.

The main floor closet is to the left of the front door, not in the correct spot to add insulation.

After adding insulation between the floors we could replace the living room ceiling. Maybe access doesn't need to be permanent.

Here is where we are making changes to the staircase. Its cold and breezy in this spot.

Sorry, I misread and didn't catch the part about it being a two story, bedroom above. I know it's possible to blow in insulation in wall cavaties with little disturbance to the inside wall coverings,(plaster, drywall, panelings, etc.), but I don't know if it's possible to do it in ceilings. You might contact reputable insulators in your area to see about it with estimates. It might be less than removing the ceiling materials and insulating yourselves. Nice home!

You do not have to leave an access for a one shot thing.

Cut the drywall, add the insulation, repair the drywall.