Those are great areas - I'd definitely widen your search to include Mortlake and East Sheen. East Sheen has great high road amenities, pubs, a waitrose and a fantastic butcher's! It has the benefit of location with Richmond Park on side and the river on the other. Sure, these areas rely more on bus and trains, however you could easily ride your bike to work every day and have the benefit of being right by the river - riding to work on the tow path is really fun! Especially when it rains -- muddy mountain biking after a long, hard day? Yes please.
Would you up your budget if you didn't have to pay for public transport? Something to think about as there is usually something going at the Kew Riverside development next to the archives.