Thanks all. I was starting to suspect the filter after reading threads, especially after seeing some comments about "Newton's Rings" and some artifacts that occur most prominently on green light. Though these don't look like Newton's rings. I have a cheapo Canon Philippines filter that I purchased used for about $5 to protect the lens. (Way to devalue my investment I know.) I was associating these streaks with general image softness as well. Sometimes this lens has great, crisp shots, and sometimes they're soft as hell even at a pretty good speed and aperture, as noted by phreeky. And not in a way that matches up with any other tests done on this 70-300. I felt like I was getting some of this effect when I tried removing the filter but I wasn't testing it in a controlled way -- these might have been in lower light situations with my aperture wide open at 300mm with camera shake too great for IS to deal with. I think my first step is to do more controlled testing with and without this filter, and especially with green backgrounds at distances.
My other suspicion is camera shake like TheBurningCrown mentioned from pressing the shutter and my camera moving down some, but in reviewing these photos taken from different scenarios I realized that the lines only seem to appear on green, forested areas.
xarqi, it's not the DO lens (I read about some artifact issues with that). I'll do some more tests with the IS off though, I think I also tried a few test shots that in situations that were too low-light.