...In the OP's situation, I'd size up the London Hilton's premium. If (1 night London Hilton+tube to LHR < Paddington+HEX+cab fare), the choice is clear--LONDON HILTON, and use the bus or tube, but skip the HEX. But otherwise, if you haven't tried the Paddington, you might save a bunch, see a new neighborhood, and slip seamlessly to LHR on HEX. Might even try 2 nights at Paddington (my choice, usually, and then hold my nose for the HEX fare, or STILL use the tube if I'm travelling light and by myself).
I don't understand why you don't mention Heathrow Connect. It's WAY cheaper than HEX, a little bit slower (as it makes a few stops), and runs less often. But it can be a reasonable substitute for HEX.
No need to "hold your nose for the HEX fare." Just use Heathrow Connect instead.