Limited Bandwidth and Order of Arrival The new audio file mentions how they have limited bandwidth available with which to transmit the data with, this explains why the audio is slightly corrupted. This does not explain why the audio seems to be arriving in a strange order, or why the audio is slightly shifted around and does not properly match up.
Yellowstone Super-Volcano The audio mentions the Yellowstone volcano, this changes the hypothesis to factor in that a nuclear war would not have as such a huge effect on the population in such a short amount of time to wipe out ~6 billion of the population in less than ten years. The actual magnitude of the last Yellowstone eruption was 675000 megatons approximately, this is orders of magnitude higher than the combined destructive force of all nuclear weapons that mankind has. If the volcano had erupted at some time during the years 2250-2275 then it would easily explain the huge drop in population for two reasons. Reason one: the eruption itself would have a huge explosive force and most likely destroy most of the mainland united states within a few hours. Reason two: The amount of debris created from the explosion would be unparalleled and completely change the climate and conditions around the globe. The most recent eruption 640,000 years ago ejected 240 cubic miles of pyro-clasts into the atmosphere, this would cause huge drops in temperature and also not allow plants to get enough sunlight to grow sufficiently or at all, culminating in what is essentially a nuclear winter and global dimming to the extreme. Currently the Yellowstone caldera is rising at 1.5cmyear^-1 which implies that pressure is building in the magma chamber and that an eruption is imminent in the next few hundred or thousand years, and the caldera itself is 55 by 72km, this means the volume of the caldera has risen by is 1.4*10^10m^3, if it erupts at the time shown to coincide with the massive population drop on the graph then this would be the main cause of temperature rising and then dropping suddenly. It also eliminates certain locations that the transmissions could be coming from as they would be completely changed geographically and probably still molten and changing.
Current contradictions
Scientists currently estimate that roughly 6-8% of the magma chamber is molten rock, and that this eliminates the chance of the volcano erupting soon, but evidently these transmissions say otherwise, what caused the eruption could be nuclear war with multiple warheads hitting the caldera and causing mini eruptions that then chained together to cause the eruption of one of the calderas. The eruption of Yellowstone would possibly trigger the eruption of other volcanoes due to seismic activity it would generate, this would mean the debris would be orders of magnitude higher than currently estimated, especially if the pacific ring of fire erupts, while they are not explosive volcano, the amount of SOx gasses released would have a huge atmospheric impact.
Spectrograms
The above image shows all four audio transmissions lined up to show which parts are connected and fit together to give the whole transmission. With the fourth transmission showing the context for Yellowstone.
Sources; https://en.wikipedia.org/wiki/Yellowstone_Caldera https://volcanoes.usgs.gov/volcanoes/yellowstone/ https://www.yellowstonepark.com/things-to-do/yellowstone-supervolcano