For what it's worth, we recently did this same stay (one week, presumably at the DoubleTree Ealing?), and if traveling off-peak the Tube option was pretty easy to/from LHR to Ealing Common. It does require a change of trains at Acton Town, but there are elevators to cross over to the other platform to head back out one stop on either line to Ealing Common. This has the advantage of not having to worry about schedules on TfL rail, and also is only 1.50 GBP. We were helped by arriving on a Sunday, departing on a Saturday morning, though the Saturday morning 05:48 Piccadilly train on Saturday morning was the most crowded of all four used to/from LHR. Ride time was about 30-40 minutes IIRC via Acton Town. Unless you're traveling very lightly, I'd assume you'd want to transfer from TfL Rail to District Line at Ealing Broadway to get down to Ealing Common, so you're looking at a change of trains either way. The walk from Ealing Broadway to the hotel was quite easy without luggage, but I would not have wanted to do that to/from the airport.
In five days travel to/from central London and around, we ended up hitting the 8.00 GBP cap each day. The arrival and departure days we didn't travel more than the one airport trip so just had to pay the 1.50 each for those two days.