I wash my truck almost the same as you except for this:
I start with the tires. I use Spray Nine and a soft scrub bush on the tires to get the heavy road scum off. I also do this to my chromed steel wheels (not recommended on aluminum since it sratches the clear coat). This gets my white raised outlined letters very white. After washing the whole truck I go over the tires and wheels with the sponge. Results are excellent. This process takes off everything including tire dressings.
