I doubt many Spectrum ads called it the 'Speccy' but we called it that anyway.
Yea, searching for how it was used in ads is a bit silly imo. It'd be like someone looking back going "I can't find any evidence of it being referred to as a PS2 back then... all the ads are saying PlayStation 2!".
Check more informal usage on UK TV, and you'll find it being called a "snez" constantly. https://youtu.be/hkgcg4pRsaA?t=4m36s