Great question — answering as the UphillTech team:
Do not coat the entire face of the drywall with compound to make it thicker. That is really hard to get right and will only serve to frustrate you. The way I see it, there are three options here that I would consider in your situation. If I have to replace drywall in a room, replace all of the drywall. This is a bit of extra work, but the end result will be really good. Plus, it provides an opportunity to inspect wiring, plumbing, insulation, etc. that is covered by the drywall and repair anything else that needs it in the process. You can also make improvements such as adding outlets or switches. Shims behind the drywall, which you already mentioned. This is probably the easiest way to get...
Full answer by user4302: https://diy.stackexchange.com/a/117824 (CC BY-SA 3.0).
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