To be honest I think you are overthinking it a little. It is pretty straightforward. I personally wouldn’t bother with a car.

If you do want one the most common way in London by far is Uber, though there are reports of Uber drivers at Heathrow calling riders and cancelling when they find out they just want to go somewhere close to the airport. The only other company with any kind of scale is Addison Lee.

Edit: Good suggestion about the bus above. Visitors seem to get a little worried about them, but London buses are some of the most straightforward anywhere. The bus is also free within the Heathrow area whereas you will have to pay for the tube to Hatton Cross.

Also if your rate is cancellable then worth knowing that a new Hilton Garden Inn is opening close to terminal 2 and 3 in February. It’s not open for booking yet but worth keeping an eye on https://hiltongardeninn3.hilton.com/...EGI/index.html