26 minutes for the fastest time to London Paddington and 32 to Tottenham Court Road.
I know you probably know this, but this is probably a good post to reply with comparison.
Heathrow T5 - Paddington (Hex) - 20 Minutes - 1 Stop
Heathrow T5 - Paddington (Elizabeth) - 31 Minutes - 4 Stops
So you are paying a fortune to save 11 minutes (the frequency of the Hex helps of course)
But then for other significant underground stops
Bond street (Central, Jubilee and Bakerloo) - 35 Mins
Tottenham Court Road (Northern) - 37 Mins
Farringdon (Thameslink, Hammersmith and City) - 40 Mins
Liverpool St (Northern) - 42 Mins
Going from Heathrow Central
Heathrow - Paddington (Hex) - 15 Minutes - 0 Stops
Heathrow - Paddington (Elizabeth) - 27 Minutes - 6 Stops (26 minutes on the "faster" service)
Bond street (Central, Jubilee and Bakerloo) - 31 Mins
Tottenham Court Road (Northern) - 33 Mins
Farringdon (Thameslink, Hammersmith and City) - 36 Mins
Liverpool St (Northern) - 38 Mins
Canary Wharf - 45 Minutes
I suspect if you are going further then Paddington you won't have boarded the relevant onward travel in the time you have saved from the faster ride to Paddington. I don't know what the interconnection is at many CrossRail stations such as to the Jubilee line at Bond Street. But a assume it is possible to do everything without hitting stairs.
Source was Real train times (East bound only) - Maybe we could try a few forum "races" to popular London destinations. One on the Piccadilly, on on Hex and one on Cross Rail. The Piccadilly line may not be a slow as some think. I have at weekends used the HeX and wished I had taken the Piccadilly line. For me a single change at Finsbury Park can be more desirable then the changes at Paddington and Kings Cross that HeX previously involved. But I just can't see any circumstances would ever save time (Or have any other benefit) using the HeX. I am sure that it will still get passengers who prefer it, just like Gatwick Express seems to live on despite it saving even less time compared to HeX. If it can make enough money for these, that is a different question. I have never understood why people pay to go first class on the Hex for such a short journey - but they do.
Just so I am not contradicting Starmill - Tottenham, all stops upto Liverpool Street can be done 1 minute quicker if you use the service that stops at 3 stations, rather than the all stops I quoted. Going the other direction the "faster" Elizabeth line service takes just 23 minutes, so the HeX is saving a stunning 8 minutes from London to the Airport.