Lightroom: I would love to see an advanced renaming tool

It would be great to have this within LR itself. I'm sure I've seen requests for such in the past so hopefully, at some point, they'd work on it. In the meantime, you can try John's plugin - http://lightroomsolutions.com/articles/complex-file-renaming-in-lightroom-made-simpler/

The file rename tool in LR Classic, does allow you to use just the 4 digit original file number as a component of a newly constructed file name.  

For example, this template takes my RAW file name such as "IMG_1234.CR2" and changes it to  "7d2R03-#1234.CR2".

My biggest annoyance when renaming files in LR is when I have one or more file that has been also edited in PS.  When I want to save the original filename number suffix it only uses the number that is after the dash.  In other words, each LR file that is worked on in PS then saved back to LR gets an extension number preceded by a dash.  When exporting all the files, LR uses the numbers that come after the dash rather than the original file numbers from the camera.  I wind up having to go manually into the folder of exported images and rename each of those files by hand.  Maybe I'm just doing it wrong and there's an obvious solution so this seems like a good place to get a recommendation on a better way.

Did you try the "Original number suffix" field in the rename template?   Also,  if the images you edit in PS come back as a different file type (Tiff?  PSD?) you can filter on the file type and have one template for the original RAW files and another template for the edited version.  You can also look for the "-edit" on the file name to filter the returned images.   

An actual example of this problem would help us be more specific rather than talking in generalities.