I checked out the PDF for your GH Aero System.
I guess I'm confused as to what their trying to accomplish.
My First Hydro System I built was combination NFT with Mini Sprayers inside which I would guess is similar to this systems operation/goal.
If your sprayers are getting your roots wet, there really shouldn't be much of a need to soak the roots in a deep
nutrient. Once the roots reach the bottom of the trough, you shouldn't have to worry about them being soaked.
I'll see if I can find the pictures of the one I built.
I'm still guessing that Oxygenation of your nutrient fluid might help.
Also, if you do have a problem with heat..that could be a problem also wit the root browning.
Also, I'm not sure, but I thought I read something that the system was designed to be grown/used under artificial lighting, which would suggest indoor use, where room temp. would be more likely controlled, suggesting to ME that you wouldn't have to worry about outside heat spikes in temps.
Oh, before I forget...
How were your plants started? From seed in a hydro-friendly medium?
Or Soil, then transplanted to your system?