Carbon backup discovery issues with Nexus 7
As it turned out, all the other apps had their corresponding .json file missing. Not a big deal: As badp's answer shows, one can simply use adb restore to restore the backups. But as not everybody might have the SDK (or even a minimal ADB) installed (or even a computer available -- one might be on a journey), my answer will take a different approach.
What we need
First, you will need to make a backup of some app, to get a working .json file. As the question states, there was such one from the Adobe Reader. To visualize it for you, this is what the corresponding file (com.adobe.reader.json) looks like:
{
  &quot;enabled&quot;:true,&quot;system&quot;:false,&quot;flags&quot;:10010180,&quot;packageName&quot;:&quot;com.adobe.reader‌​&quot;,
  &quot;versionCode&quot;:73784,&quot;label&quot;:&quot;Adobe Reader&quot;,&quot;versionName&quot;:&quot;10.5.2&quot;,&quot;locked&quot;:false,
  &quot;date&quot;:1367072517125,&quot;apk&quot;:false,&quot;‌​backup&quot;:true
}

You will also need:

a file manager
an editor

Of course, you could also perform the steps below from your Linux computer; using a different OS, take care for the file's encoding and line breaks.
What we do
I pick an example app here: Kindle for Android. In the question's screenshots, it's listed close to the Adobe Reader as com.amazon.kindle. For your apps, just pick the corresponding values based on this example:

copy com.adobe.reader/com.adobe.reader.json to com.amazon.kindle/com.amazon.kindle.json
open com.amazon.kindle/com.amazon.kindle.json with an editor

replace com.adobe.reader by com.amazon.kindle for packageName
replace Adobe Reader by Kindle for Android for label (actually, you can put anything here -- but might prefer to know what you've got :)
optionally, replace the versionName accordingly (it will work without)
save the file



I'm not sure what versionCode or flags stand for, so we better don't touch those. We also can safely ignore the rest:

&quot;enabled&quot;=&quot;true&quot; should mean &quot;this app is enabled (i.e. not frozen)&quot;
&quot;system&quot;=&quot;false&quot;: It's no system app (matches: Kindle is no system app)
&quot;locked&quot;=&quot;false&quot;: This app is not &quot;protected&quot;
&quot;date&quot; obviously holds a Unix timestamp (most likely that of the backup)
&quot;apk&quot;=&quot;false&quot;: Ah, data only (Cabon's default is to not include the .apk with the backup, to speed things up)
&quot;backup&quot;=&quot;true&quot;: Is this a joke? What else could it be?

Now, first let's see whether Carbon accepts our trick. If it correctly lists up Kindle for Android as being available for a restore, you might want to repeat above steps for your other backups as well.