I like it with the black border. Without, it's definitely too squished. And even if you cut the blocks down in size I think it still loses something being that small.
For the shadowing - you can always cut the panel out, after you applique the blocks on, so there is no fabric (or just a 1/4" frame) behind each block. Or, some fabrics are denser than others. Kona hides colour pretty well, Michael Miller shows everything for example. So maybe a different fabric? Even, as someone said, a beige might help and won't show beige. Pick something that you can't see your hand through, turn it wrong side up (to hide whatever colour it has as much as possible) and put it behind the light fabrics.