I went ahead and wrapped the store packages in aluminum foil. There was some frost on the inside of the plastic, but the meats still looked red (beef) and pink (chicken), so I doubt lasting harm was done.
That will help a lot.
If there was frost on the packaging, then it’s evidence that they would be freezer burning soon enough.
Since the meat looked good, then it was likely just moisture inside the package and not freezer burn.