Q:

How do I find the fastest route from Heathrow to an address in London using all forms of transport?

Neither Google Maps nor Traveline.info seems to consider neither Heathrow Express nor cabs. Is there any service that would?

A:

Citymapper, also available as an app for iOS and Android, has never failed me in London or other large cities where it is available. Cabs, Uber, Tube, buses, Heathrow Express, cycling, walking, I don't know of any mode of transport they don't cover, at least in London. The mobile app (but not the website) even finds a combination of public transit and cars-to-hire (scroll to the bottom of possibilities offered): 

It also shows you the cost and the time of any alternative routes it finds, the best place to be on trains, as well as the best entrances and exits for tube stations. And it calculates time for transfers inside the stations.
It's my most important app whenever I'm there.

A:

The simple answer is that depending on the address Heathrow Express or a taxi may not be the fastest way to get to your address and routing apps are taking that into account.
London is highly congested, road speeds are often  8mph for cars, so taxis can get stuck in that traffic.
Heathrow Express goes into Paddington Station on the western side of central London, which is fine if you have accommodations on that side of the town. However if your destination is elsewhere by the time you have got off at Paddington and then found the correct route to continue your onward journey the time saved by using the Express can be eaten up. 
If you can give us some idea of where the address is further it may be possible to give more focused help.

A:

On Google Maps the Heathrow Express will show up if you specify a terminal to depart from.

As for Taxi journeys, time wise those would mostly be equivalent to the Car timings on google maps.

