ex drywall contractor here, it will be a pain in the ass and messy but skimming the existing surface would be the less troublesome way to deal with this. Will probably take a few coats. Get a wide blade, a wide mud pan and topping mud (not taping or all purpose mud) because topping has no glue in it and its easier to sand.
Pull it tight and sand lightly between coats, you can finish with a damp sponge instead of sandpaper to get a smoother finish.
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“Ours is a world of nuclear giants and ethical infants. We know more about war than we know about peace, more about killing than we know about living. If we continue to develop our technology without wisdom or prudence, our servant may prove to be our executioner.” ― Omar Bradley (1948)
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