I like your thoughts on everything except the screens 
I have never yet seen anyone be successful with any type of screen as far as getting roots to make good use of it. Well, the exception is one or two cases for stability and support.
I recently saw a post by Atomizer where he is using a screen in a trough to support his plants, but it is just to give the roots something to hold onto for stability because he is not using any kind of net pot. His atomizing system uses hi pressure to blow the droplets all around and he isnt worried about loosing some droplets to the screen. You have the net pots serving the support purpose already, and he did not.
Im pretty sure that article you read was talking about the screen collecting condensation when the air reached the dew point in an environment with low relative humidity - like a desert environment or some other relatively dry place with little to no rain.
Inside your totes will be as far from that as possible. The humidity is gong to be at or above 100% as long as there are no air leaks, so there will never be condensation or dissipation in the way that article was talking about.
The screen will collect droplets, but not in the sense of recovering the moisture as the fog dissipates/evaporates away. Instead, those screens are going to grab droplets out of the air as they pass by - which will keep them from getting to the roots.
Your droplets are NOT dissipating. They are going away because they hit something and stick to it.
All the screen will do is reduce the number of droplets floating around that much faster. You will be adding one more thing for them to collide with and get stuck to that isnt a root.
Remember your primary goal with any type of aeroponics is to create a UNIFORM environment of droplets in which the roots can have the ideal mixture of O2 and nutes. Ideally, that environment needs to be as uniform and consistent as possible.
In most aero setups, you end up with a wet/dry cycle. The nozzle ON cycle sprays too much water onto the roots making them too wet, which deprives them of oxygen. Then there is the OFF time while the roots dry out - often becoming too dry. That wet/dry cycle can be made to work, but is not ideal.
According to NASA, the ideal environment is composed of 20-80 micron droplets - but - you dont want the mist too wet or too dry. You want it to be as uniform and unchanging as possible - AND - at just the right balance between wet and dry.
To achieve that balance, you need to juggle the flow rates and ON/OFF times of the misters, nozzles, or foggers that you are using to create that environment.
Too hi a flow rate and the roots get soaked during each ON cycle. Too low a flow rate and they never get wet enough. Too short an OFF time and the roots are back to too wet, and too long an OFF time makes them too dry. You need to juggle the flow rate and ON/OFF times to get to those numbers I quoted by Atomizer above. Each system is different, but his numbers will get you in the ball park. Then you have to look at the roots and the plant to dial it in.
It looks to me like your roots are telling you that they are pretty close to being happy. You are getting new white growth and fuzzy hairs, so you are at least in the ball park as far as that environment.
It sounds to me like you are worried about the center, or the under side of the root mass not getting enough mist? You dont really need to worry about that. Those small droplets - especially the ones you are making with the foggers, will easily penetrate into the root mass.
Take a look at the pics of my roots above. They are not all smashed to gether like you see when you pull a mass of roots out of a DWC bucket. There is tons of open space for those micron sized droplets to pass through.
All you need to do is provide enough of those droplets - but not too many. You want it to create the Goldilocks environment - not too much and not too little, but just right
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