I realise it’s missed the boat, but face fix Blum type concealed hinges would have been ideal in this situation and would have avoided having to apply any rebates. Here’s the link in case it’s of any use in future;
https://www.swanseatimber.co.uk/pdfs/Ca ... _460_M.pdf
https://www.swanseatimber.co.uk/pdfs/Ca ... _460_M.pdf