I don’t think this is possible. The Shotcut clipboard is internal to the app. It isn’t the operating system clipboard.
Your app looks great!
I finally got a chance to try out your MLT file and apply some filters to it. I was able to get sets 5 and 6 looking much closer, but it was not a fast process.
From what little reading I’ve been doing, it seems that GoPro in flat mode has different gamma curves per color channel, which effectively multiplies the effort using scopes by 3x. I can’t verify that’s true, but it sure felt like it. I had to consistently pull red down in the highlights and green down in the midtones.
Once I got sets 5 and 6 working, those values did not apply uniformly to any other sets. I’m guessing one or more cameras was in Auto ISO mode, which is usually necessary when outdoors. So, the work kinda has to start all over again for the next clip.
For your use case, your app is probably the fastest way to get a match.