Hey @jmanford8 and @paulkelbin
Found a solution as this thing is really super annoying and shows real browser companies attitude to your attempts in getting some privacy.
My thoughts were: if there are no extensions that can really clean browser data as needed (and I found no one that removes this address bar suggestion shit), we can simply not allow browser to capture the history.
And the first extension in the market "History On/Off" performed excellent! No history at all, yep. That's not for everybody. But no suggestions also!