Can't get CC below 0.5 ppm

I've SLAMmed it several times, and the best I can do is 0.8. If I don't SLAM on the reg, it will be between 1 and 2. I figure I must be doing something wrong for my setup.

Here are the factors that I think are influencing my process:

1. My < 1 year old tub came with an ozonator
2. It's under a tree that drops a lot of dried up blossoms, leaves and other organic matter, seemingly all year long
3. It doesn't get much sunlight.
4. It has very low bather load (about 5 person-hours a week)

I've messed around with the following while SLAMming:

1. Keeping the lid closed to keep the tree stuff out. I figure if I've got a lot of organic matter in the tub, my FC is perpetually trying to oxidize it leaving me with a baseline of CC greater than 0.5.
2. Keeping the lid open to deplete the CC via "gassing off" and what I would assume would be a marginal amount of sunlight-driven decomposition.

Is this a "Darn if I do, Darn if I don't" situation here with the lid? Is there anything else I can try?

If there's not really anything I can do, is it really that bad having CC levels in the 0.8 - 2 ppm range? There isn't any strong chlorine or other unusual smell and my water is crystal clear.

Thanks in advance for any help