I tried this on my ES920 which also has the RH-III action. I also found the black keys are easier to play near the fallboard than the white keys.
I've never noticed a problem playing deep into the white keys. Just messing around a bit it seems like a Bb chord played with pinky and thumb on the Bbs and fingers 3 and 2 on the D and F is a worst case scenario:
Playing the whole chord feels fine. If I weren't thinking about this issue I don't think I'd notice at all. If I play the notes one at a time the D and F feel a little awkward. But I can't tell if it's just because I'm now aware of the weight difference or if there's really an issue here!
I'm away from home so I can't compare on my acoustic piano right now but I'm eager to do that when I get back!