No idea about the Uxbridge service but I recall something infrequent (possibly half hourly) Baker Street to Amersham via Watford and the North Curve. However, limited stop / many stations missed out... it was great, not so much zooming through downhill stations such as Chorleywood as 'storming' through at full pelt which as this was a downhill gradient could easily have been well over 70mph. Maybe even something like 80mph! Rickmansworth was one of the station stops, which perhaps was just as well with its restricted line speed.
I have some super 8 film from inside a train, but its just too unsteady to view.
As an aside, at the London end services were also limited stop and this included missing out Barbican and Farringdon. This was on a C stock train but I dont recall whether this was operated by the Met's Hammersmith & City section or as a Circle line working.