I just read through this thread.. Interesting problem to figure out. To answer your question. YES an IC40 is more than adequate for a 13K pool... and YES you can install multiple SWG's in parallel. Some controllers support that, some don't so you would have to add a second controller....
That said what else could be chewing up your FC in hot conditions. .. that what's what it boils down to.. You can throw more FC in there via jugs of LC or 47 SWG's wired in parallel to compensate but, we still haven't solved the mystery of were the FC is going. You say it happens when it gets hot or when it gets sunny? those are two different conditions.
So to throw my 2 neurons worth of brainstorming into the mix, I am reminded of the pool owner that could not figure out where is chlorine loss was until he posted some pics of his custom water features and sculpturer friend of his did (or something like that). But it turns out they had large bowls that retained water in the water feature and were a perfect breeding ground for algae growth. Do you have some kind of water feature or something attached to the pool that would behave that way?
Thanks for the response.. No no water features.. Just a rectangular relatively shallow pool (~4.5' deep average) with a spa. The pool stays pretty much pristine....