Sorry, I don't know what to tell you. If your Z2 is faster than a Nexus 5, and my Nexus 5 gives instantaneous results when using Google Search on the web or the phone, then I don't see how it can be way slower than Spotlight. Is tapping the Google Search Bar and then starting to type really that much slower than swiping Searchlight over and starting to type? It'd be interesting to see a side-by-side comparison.