This is the route. Not sure how the formatting will work. I found the TfL timetable to be reasonably accurate at estimating journey times between stations. There a few places where this route doesn't work, e.g. Moorgate-Bank covered twice, King's Cross visited 3 times etc.
Depart dep Arrive Route Actual
Upminster 04:58 Aldgate East District 0
Aldgate East 05:38 Aldgate run
Aldgate 05:44 Gloucester Road Circle 0
Gloucester Road 06:11 Russell Square Piccadilly
Russell Square 06:27 Holborn Piccadilly
Holborn 06:40 Hainault Central
Hainault 07:28 Woodford Central
Woodford 07:41 Epping Central
Epping 08:02 Leyton Central
Leyton 08:25 Walthamstow Central bus
Walthamstow Central 08:52 King's Cross Victoria -6
King's Cross 09:13 Cockfosters Piccadilly -1
Cockfosters 09:50 High Barnet bus 0
High Barnet 10:17 Finchley Central Northern
Finchley Central 10:43 Mill Hill East Northern -11
Mill Hill East 10:48 Camden Town Northern
Camden Town 11:11 Edgware Northern -5
Edgware 11:39 Canons Park bus
Canons Park 12:00 Stanmore Jubilee -13
Stanmore 12:06 Baker Street Jubilee -14
Baker Street 12:39 Moorgate Circle/H&C -12
Moorgate 12:54 Bank Northern
Bank 13:00 Canning Town DLR
Canning Town 13:22 Waterloo Jubilee -13
Waterloo 13:43 Camden Town Northern -11
Camden Town 14:02 Elephant & Castle Northern -12
Elephant & Castle 14:25 Lambeth North Bakerloo
Lambeth North 14:30 Elephant & Castle Northern
Elephant & Castle 14:35 Stockwell Northern -14
Stockwell 14:47 Brixton Victoria
Brixton 14:51 Stockwell Victoria
Stockwell 14:56 Morden Northern -18
Morden 15:20 Wimbledon bus
Wimbledon 15:44 Earl's Court District -23
Earl's Court 16:08 Kensington Olympia District
Kensington Olympia 16:12 High Street Kensington run/bus
High Street Kensington 16:25 Edgware Road District/Circle
Edgware Road 16:34 Edgware Road run
Edgware Road 16:39 Oxford Circus Bakerloo
Oxford Circus 16:49 Vauxhall Victoria
Vauxhall 16:59 Waterloo rail -18
Waterloo 17:09 Bond Street Bakerloo
Bond Street 17:19 West Ruislip Central
West Ruislip 17:55 Ickenham run
Ickenham 18:09 Uxbridge Piccadilly -19
Uxbridge 18:17 Rayner's Lane Piccadilly -21
Rayner's Lane North Ealing
North Ealing 18:48 West Acton run
West Acton 18:58 Ealing Broadway Central
Ealing Broadway 19:07 Acton Town District -10
Acton Town Heathrow Terminal 4 Piccadilly
Heathrow Terminal 4 19:53 Hatton Cross Piccadilly
Hatton Cross 20:10 Richmond bus
Richmond 20:48 Gunnersbury District
Gunnersbury Chiswick Park run
Chiswick Park West Kensington District
West Kensington 21:10 Hammersmith District -20
Hammersmith 21:15 Hammersmith run
Hammersmith 21:23 Paddington H&C
Paddington 21:36 Paddington run
Paddington 21:41 Harrow & Wealdstone Bakerloo
Harrow & Wealdstone 22:14 Kenton Bakerloo -2
Kenton 22:19 Northwick Park run
Northwick Park 22:25 Preston Road Metropolitan -2
Preston Road 22:30 West Harrow Metropolitan
West Harrow 22:39 North Harrow run
North Harrow 22:53 Watford Metropolitan
Watford 23:18 Moor Park Metropolitan +1
Moor Park 23:38 Chalfont & Latimer Metropolitan +31
Chalfont & Latimer Amersham Metropolitan
Amersham Chalfont & Latimer Metropolitan
Chalfont & Latimer Chesham Metropolitan