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Wes, I hope you don't mind, but I did a quick and dirty process of your image. The reason why I suggested that it might've been the filter you're using is because when looking at your file I noticed an imbalance in your channels. This suggests to me that you might have had to remove a colour cast, one possibly produced by your filter. Since the loss of data was in the green channel I'm guessing that the cast was probably a cyan/green colour? Now is it the cause for the grid pattern you're seeing? I'm not sure because after taking a second look I saw that the grid pattern runs throughout all three channels, but it could still amplify the artefact which isn't desirable either.
The good thing is that you've managed to capture a solid amount of data and because of that I was able to reconstruct some of the missing information. Although you can't create what isn't captured you can sometimes synthesise (fake what's missing) which is what I've tried to do here. Essentially I replaced (or guessed) all the tones that I thought were missing from your image to try and balance out your histogram. It's not perfect and by no means scientifically accurate, but hopefully it gives you an idea of what can be done with a channel rebuild. As the others have suggested dithering your subs would really help so, when processing this I attempted a simulated dither to see if I could mask the grid pattern. It's still there no doubt but hopefully not as obvious as before. However, remember I'm doing this as an after thought to an already processed image. If you do this with raw data your results will be a lot better.
I hope this helps.
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