@Jossie to get an answer worth anything we must see the files in question:
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Resize the scanned images in your scanning software to something small and easy to download, e.g. 100x100px (or just scan a patch at that size), one with the embedded profile and one without, and upload both using some lossless file sharing service like https://filebin.net/
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When I open them in PSE and save them again as Adobe RGB
Upload these two as well.