I use the pasteboard for sending data between applications as well. It's a really useful tool for sending medium size amounts of data between applications. I actually wrote up a blog post on the topic a while back.
Unfortunately, as you've pointed out, private pasteboards are only available to apps that share the same prefix in their app id. This is typically the Team ID, but may be different if you have an app that dates back to when you could use a different bundle seed identifier.
If you have medium sized amounts of private data being shared between apps with different prefixes then a different solution is in order. In this case I would suggest using some form of encryption and using the general pasteboard to shuttle the data around. Depending on the sensitivity of the data, it probably would be a good idea to encrypt the data even when using a private pasteboard. Rob Napier has a nice library for making the encryption and decryption very simple.
Alternatively, if your data is fairly small you might consider encoding the data into a URL and using a URL scheme to move the data into the other app.