Inability to transfer Emails from one account in Thunderbird to another account in the same Version of Thunderbird

This has always been allowed in Thunderbird. Assuming these are IMAP accounts, just select the messages and drag them to a folder in the target account to MOVE them there (hold <Ctrl> to copy rather them move.) You can also select the messages, right-click, and chose "Move To" or "Copy To".

However, I think this isn't an action that is well-supported by some email systems and if you are moving many messages to the target, you may find that it chokes on the transfer after a while. That's why I would recommend you do it in small batches. It's maybe even safer to first save the bigpond messages to a Local Folder, them copy them to gmail in batches. This is just to safeguard against data loss.