Whilst I cannot spot a specific mention consistent with the details provided via
https://air-britain.com/pdfs/militar...and_and_NI.pdf a closer look by the OP might be worthwhile, as well as seeking information from the Edinburgh Evening News and The Scotsman. As an even longer shot,
Edinburgh History - Portobello - 1920s to 1950s might also be worth a look. It's certainly a trip down Memory Lane for Embra folk!
I do recall my Father telling me about a forced landing on the farmland immediately to the North of Lauriston Castle in my native Edinburgh, probably in about the mid 1950s, but that land is more of a raised beach than the beach at Party, and I also have a feeling that it was a twin-engined aircraft, and possibly even an Anson.
Jack