According to the marriage certificate they were married at the Rutland Hotel, Rutland Street, Edinburgh which is in fact just outside St Georges; you can see it on the map that I linked to, across Lothian Road from the marked church of St Cuthbert's.
Their addresses were 3 Leslie Place and 26 Drumsheugh Gardens, neither of which is in St Georges nor in the Calton area.
If you send me a PM with your email address I'll send you a copy of the certificate.
Added: see below reply #8 – I no longer think this is the correct marriage. Apologies for confusing the thread.