Did the nose and tail fairings, and lack of a mid-upper turret, significantly improve the Lancastrian's performance, compared to the Lancaster?
Seemingly so. The fast freighters run by BOAC in the late 1940s from London to Johannesburg and Sydney with just a handful of stops (tables 30 and 31 here), albeit lengthy overnight stops (probably the same crew throughout) were done with legs of around 2,000 nm, which I guess is well beyond a standard Lanc.
http://www.timetableimages.com/ttima...49/ba49-09.jpg