So now we know that you use CryptoBit wallet and store it's file/backup locally. While source code for CryptoBit exist, i didn't find any documentation or relevant article/guide from Google Search. So i think the next step is either,
1. Read source code to understand how it store private key on generated wallet/backup file.
2. Compile the extension from source code, then load it manually to Chromium-based browser. Afterwards, check whether the extension have option to restore or load the backup/file.
But i don't have such skill or experience to do either of those.