Of course. I'm glad it might be helping you troubleshoot. Buffy's symptoms were vague yet unsettling. In retrospect, she was always the first to breathe mouth agape and the last to stop on warmer days. That was a sign.
I now have an inkling that, especially for hens bred to mature quickly, heart issues are more common than acknowledged (interestingly, I read that necropsies done on 2 year-old production hens like ISA browns found organs that were flabby and darkened--yet other breeds of the same age showed little internal wear). I'm not a doctor though so grain of salt!
The one thing I learned to be extra vigilant about w/ Buffy is to monitor her feed intake. We almost lost her because, by the time she was showing visible signs of distress, she was refusing to eat altogether. Buffy had likely been consuming less and less over the past week from accumulated heat stress and we didn't notice, which was further preventing her system from bouncing back. Once she was force-fed at the vet's her appetite came right back (and she was vibrant again in no time). Make sure to keep an eye on your hen's eating habits and weight so you don't get to that point. Wasting can accompany heart issues.
Also, if you're able to build a temporary pen (or put her in a large dog crate) someplace cool like in the house or basement--only for those peak hours of the day--it might be enough to take the edge off. We even pair Buffy with a friend sometimes... In this heat it's kinda like a girl's spa trip (or reverse sauna!).
Anyway, I'm sure you've already considered the above and then some. I hope your hen is getting better. It's frustrating to watch them suffer and not be able to tell you what's wrong! I hope you find more answers--and please do keep me posted.
P.S. Thank you for the heartening cat anecdote. Sounds like she had a good, well-loved life