I wonder if it was actually a NOTAM about the AIAA that popped up. The way SkyDemon handles popups on airspace, P/R/D areas and such is pretty similar to the way it handles NOTAM information. So all SkyDemon may have done is warn you about "airspace ahead". (Does anyone know if there really was a NOTAM about the AIAA about?)
Nevertheless, an AIAA should not come as a surprise. They are clearly marked on the paper chart as well.
Before we could execute the suggested 180 & head back, lo & behold a fast moving cloud from my 9 Oc'lock position had rapidly closed on me & engulfed us fully & everything was dull Grey....sight was lessened to ZERO
Clouds don't move independently and on their own free will. Clouds normally sit still in a (moving) block of air. And if they are moving within that block of air, then the only way they're moving is up due to convection or oreographic lift. The only thing that's really moving within that (moving) block of air is you. At 100+ knots. So you can't say that "the cloud from my 9 o'clock had rapidly closed in". Rather, you flew into a cloud that was just sitting there, fat, dumb and happy.
During your PPL training, did you ever fly close to cloud? I never did - clouds were scary things, to stay well away from. It's only when I started flying aerobatics that we occasionally flew at altitudes with scattered clouds, simply to play with them. It's very good practice because it makes you appreciate how fast the aircraft is really traveling. Something that you don't appreciate while flying in clear blue skies. (One of the most memorable exercises was to approach the top of a cloud, about 100 feet below the top, and barrel roll the aircraft over the top of the cloud without touching it. Would not recommend that in a DA40 though.)
Combine this with another thing. Cruise flying at 5000' or so, you quickly settle into what I call "airliner mode". You only make very small corrections to the controls with your fingertips, unconsciously trying to avoid even a ripple in your cup of coffee. When you encounter clouds, there comes a point when you need to switch to "fighter jet mode". You need to grab the stick with your full fist, making turns with 45 or even 60 degrees of bank, and pitch changes of maybe 20 degrees up or down, to stay clear of clouds. Especially if you're in a layer of SCT with no way out up or down.
If you don't switch from 'airline' to 'fighter jet' mode quickly enough, because you don't appreciate how fast you are really traveling yourself, you will find yourself in cloud very quickly. So an exercise "playing with the clouds" may well be very useful in this respect.
I remember looking at the TC Ball proving to be so slippery & volatile in its movement.
Did you ever do Ex19 in a glass cockpit? Because I feel you've been watching the wrong instruments, possibly due to an overload of data.
Just as with steam driven instruments, the primary instrument is the artificial horizon. The only thing you need to do is keep the dot on the horizon, and bank about 20 degrees. Leave the power setting alone and this should get you into a nice, stable, rate 1 turn. If you're in a TCu or CB, ignore speed, turn and altitude variations - they will eventually more or less cancel out. (With "ignore" I mean that it's perfectly OK to keep track of the variations, to see if they're not getting too extreme. But minor variations do not require a control correction. Just keep the aircraft in the same attitude.)
And in a DA40, the slip ball is all over the place even if you don't keep your feet on the pedals in a steady cruise. Unless my bum is telling me that I'm seriously flying out of balance, I'd ignore the slip ball altogether. Especially when overwhelmed by the circumstances.
Anyway, well done. Your PPL is a licence to learn and it seems you learned loads today. It might be worth talking things over with an instructor once the emotions have settled down, and adrenaline levels are back to normal. I think there are a lot more lessons to be learned from this.