@thecryptofiend

This information is awesome and going forward perhaps we should formalize the methods a bit more.
But your information while great is already addressed by the study's construction assuming we can get a large enough group.  It all comes down to the central hypothesis which is this...

Does interrupting the inflammatory cascade reduce the length of a depressive episode?

We aren't asking if NSAIDs can treat depression.  I'm not even sure that would be a valid question since each NSAID has a different method of action.  On the other hand, if we see a correlation in the data, then that poses a seed for further research.

The other thing is that we are only recommending people use OTC anti-inflammatories if they are in group 1 or group 3 and the first one of the drugs listed is not an NSAID and yet is one of the most common OTC anti-inflammatories.  OTC anti-inflammatories are GRAS at this point especially Tylenol.  However no one should be rushing out to buy and take something they've never heard of before.  This should be "whatever you normally take for aches and pains".

The control group gives us a baseline, and is protection against selection bias because we can safely assume that the control group will be the least likely to be depressed to the point that any of these actually sound like great ideas.  But will also have a goodly selection of people who would be any of the other groups except for time and life issues.

Group 2 are likely to be the ones most likely to see benefit if it turns out that the inflammatory response interrupt is actually a placebo effect.  The diet is one that will force the body to burn it's own fat and raise it's own metabolism and this has been shown to also reduce the body's ability tendency to enter the inflammatory cascade. Thus the group 2 and group 3 people are forcing their body to not go into the hibernation state that I believe may be central to the issue.

Group 3 are likely to see the most benefit if it turns out that the inflammatory response interrupt is not placebo effect, because they are doing everything that Group 2 are doing, plus they are tossing in an anti-inflammatory if they feel symptoms of malaise.

So yeah it's not a perfect study and it is relying on the assumption that thousands upon thousands will participate, thus drowining out issues such as self reporting biases.  However rigorous collection and rigorous analysis can let us know in no uncertain terms if the immune cascade is doing it or if it's the inflammation portion specifically, or if it's placebo effect.  At a minimum it will allow us to start the inquiry process and decide which avenues of study look the most promising.

As for someone to do the work that nobody likes doing, consider yourself hired and you can certainly author the paper and I know several places that would gladly publish.  
I'm more interested in the rigor of the data collection aspects here and making sure the dataset itself is open and the methods and procedures are well document. :D

p.s.  Please take care of yourself, that eye surgery sounds painful, just wanted to wish you well.