Here is what my voice teacher told me to help get me over that "reaching up" feeling that I had in the high part of my range. She said to pull down on the muscles of the floor of my abdomen. If you think pulling down, that also helps your breath support and if you are concentrated down there, then you are less likely to tense up in your throat. One bad habit I had was to go on my tip toes sometimes on high notes, which made it even worse than just thinking "high". I agree it is a bit counter-intuitive, but if you practice singing without thinking high or low but instead engage techniques, like relaxing, supporting, lifting the soft palate, etc., then you eventually stop stretching "up there". I assumed that I thought high because I read music and the notes go up on the staff. I tense even more if I am sight reading music and see a note "up there".

For the brighter sound, you engage the muscles in your cheeks either side of your nose and lift them. Those "snout muscles" can be hard to isolate and learn to control, but with practice, you can lift them and add brightness. Don't tense your throat while doing it, though.

Alice Flynn