the Inbox file has no extension.

This is already the answer. Mail files don't have a file extension.

I guess I also need to ask if this is a waste of time, if I have any chance of recovering the file?

Don't hold your breath.

I was just wondering if the extension was perhaps hidden. I suppose the obvious implication now is that that means I should try to recognize it by it's lack of extension. That's actually a great help. Looking at the folder again, I see it narrows the field down to only a few files.

One more question: any advice on how to examine the contents of those files? Windows doesn't know what to do with extensionless files. ... maybe give them a .txt extension and try to view them in Notepad?

Mail files are text files, so yes, you can open them with a text editor. I wouldn't try to open a Gigabyte mail file with Notepad though. There is no need to rename the file to a .txt extension, it can be opened with any text editor regardless.

I used Large Text File Viewer to check out the likely files from my recovery and no luck. I guess it was overwritten by the new one that Thunderbird created after the crash.

Thanks for your help. If you hadn't told me the mail files were text files I'd have wasted another whack of time trying to find whatever file viewer I might need.

I guess what I need to do is try to set up a script to run Mozbackup regularly because the manual method is too unreliable!