I'd first try to prove whether existing walls are beyond repair. Find an out of the way spot and use a drywall sander on the texture and/or skim coat over an area. Replacing all the drywall is a huge and messy task that involves removing and reinstalling trim. Adding 1/4" drywall is a problem as all of trim will either need to be redone or it'll be recessed which usually looks bad. And all of the electrical boxes have to be extended.

Its going to be a messy job, no matter how you do it. I would remove the drywall, and replace, because at the same time, you can check all the wiring and make sure it is all the way it should be, and you can also check the condition of the insulation, to make sure, its done right, and is in good condition, or if it also should be replaced. If trim is in good condition, take it down carefully, and write down on the back of it where you took it from, so you can put it back in the same place, once the walls are done.

Thanks, both. We're replacing the trim either way, as it's very old, brittle and full of old paint splats. So you both seem to be saying that replacement is the way to go. I'm now bracing for impact of the quotes since it is a 4,700 sqft house.

In a US house built before 1980, chances are that the wall texture is from asbestos. That’s another very good reason to remove and replace. You can have the texture walls tested for asbestos relatively inexpensively. If you or your contractors sand or cut into the textured drywall at all, it should be while wearing PPE.

It also occurs to me that if you can see seams through the paint, perhaps there were moisture issues with the drywall or the tape. Remove-and-replace would be the best protection against mold. Best of luck with your project— it’s wonderful to have so much space!