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I thought exactly that as well, but I'd struggled to sell privately for some months. My dad always used LCE so I've got some odd familial loyalty to them but never actually sold them gear before. I tried MPB who had been OK in the past but they offered me 300 for the body! I tried LCE and it paid off. Their Bristol branch is where their Leica specialist is based and he knows his stuff.
Have you tried LCE? Their office in Bristol gave me a very good price for my M6. Yours seems in far better condition. Took about 4 days, no questions or 'ooh it's not a few scratches'.