Hi Craig, I'm also a MCBRYDE from Edinburgh. Genealogy is one of my hobbies and I've researched the McBrydes quite extensively. I've traced your Newington McBrydes back to Paisley. Alexander MCBRIDE m. Marion Niven there in 1811. Eldest son Duncan McBride was christened in Glasgow in 1812 and married Jane/Jean Hamilton at Glasgow in 1837 at which time Duncan had changed to the MCBRYDE form. Duncan and Jean had quite a large family, he was a printer and moved to Edinburgh ca. 1853, where he died in 1882. Son, James Hamilton McBryde, your GGGrandfather, was a bookbinder and married Elizabeth Dickson at St George, Edinburgh in 1892.James died at Newington in 1929.
My McBrydes/ McBrides originate in Kintyre. They moved to the mainland ca. 1815. It is likely that your branch also originated in Kintyre, Bute or Arran and we may be distantly related.