I am totally new here, but your question interests me. While practicing 4 part chorales and such is excellent practice that is easy to implement as far as the reading goes, there still has to be some awareness of technique that produces results.
Just for kicks, I developed a VERY simple exercise to help with your problem. With the RH, play a CM7 chord, then a Dm7, alternating. For the first time this sequence is played, bring out the root, next time accentuate the third, then the 5th, then the 7th. You end up with a major scale being played within just these two chords. For me, the 'feel' of this is more weight on the stronger notes, but the goal is to avoid these notes from speaking first. Listen very carefully that nothing in the 4 note chords is late or early, then work on getting the voice to stand out as you move up the scale.
Speed this up to taste and according to ability. It is not a hard thing, but I think it is an oft-overlooked thing. You can then have some fun by playing simple tunes within these two chords, such as 'Shortnin' Bread' and perhaps others. Once the white keys are comfortable, do the same thing in all kinds of keys. Again, for me, the goal is achieved through more weight into the finger that needs to speak louder and this is often achieved through the slightest change of wrist position.
Hope this helps.