Looks like COLIN's theory about District-Picc tracksharing has taken a further battering ;D
On my way into the city today I saw a Heathrow service on the Picc shoot through Stamford Brook w/b local at 0920. Upon reaching Hammersmith bank I saw train 252 to Uxbridge sitting on the w/b fast, surrounded by hi-vi officials. Chucking myself off the District train I was riding at Hammersmith, I saw train 301 negotiate the freshly reinstalled 17 points and enter the w/b local platform at Hammersmith.
A quick trip in the Picc down the w/b local saw train 252 now sitting in Ravenscourt Park w/b fast with half the doors closed, as if the train was being detrained. Our train stopped and opened its doors, then shut them and ran non-stop to Acton Town w/b local.
A return trip saw several more trains performing this activity; train 252 had eventually made it as far as Chiswick Park around 0945. Oh, and the new DMIs at Turnham Green w/b appear to have the full set of District and Piccadilly westbound destinations programmed in, as it was faithfully showing 'Heathrow (Piccadilly Line)' as another 1973TS shot through