Edits to original photo file not updating in LR

Hi,

I'm a beginner user scanning 35mm negatives and importing them into LR and still finding a proper workflow. I understand the software is only a reference catalog to the original image. I want to remove film  scratches and such with PS but find the process quite tedious.

I tried to first import the images into LR and then from the software use the "edit in Photoshop function". This seems to work but upon saving the image in PS and closing the software the edited images automatically import into LR as a new image instead of replacing the previous image. Of course I can then delete the previous non-edited image but it doesn't seem too elegant especially if the edits are applied to a new image than LR creates upon export (as I understand it does when using the edit in Photoshop function).

I then tried to edit the actual original file in PS outside LR and saved it. I can't get the image with the edits to update in LR. I thought that the point of LR is that it references the actual original file? 

So in order to get around that I have to export the photo from LR (if I happen to have made edits in it), edit the image in PS, delete the LR image, then reimport the edited image? Sounds quite tedious. 

I guess what I'm asking is am I missing something in terms of a re-sync/update button that would get LR to notice the changes I just made to the image? How does the community deal with edits to the original file after import to LR?

The obvious solution to this is to scan (and edit in the scanner software) -> PS edit out all the scratches etc. -> then AND ONLY THEN at the last phase bring the image into LR as a management software utility. Sometimes you miss things and need to fix something afterwards however.. 

Thanks for your help.