I also hunt wooded areas... A couple of areas in steep canyons.
I use the terrain to hide my presence... On one place I hunt, if the bird can see me, he is probably in shooting range.
I will use the roads when I can, but am not afraid to get of the road to avoid sky-lining myself or I will walk around a large meadow or pasture if I want to get to the other side... I have game-plans for the areas I know I might be spotted, and generally take those areas a bit more carefully...
Bottom line, use the terrain to hide yourself, and avoid walking through large open areas (if possible).
I have still probably "bumped" more birds than I know... But I have had some degree of success as well. I will also stop and call while walking to make sure I am not passing a bird to get to another. When I stop and call, I do so against a tree, and NOT in the open. I might stop and call every 100-200 yards depending on the terrain, and whether or not I am already walking to a vocal bird.... If I am walking to a vocal bird, I am less apt to call as much....