I had an FSD failure just as I reached 80%. I might be unlucky.
And yes to escape, I let the FSD charge, then boost to momentarily align the vector of my ship which is enough for the FSD to catch on.
I believe there are some different events occuring. One which is basically the "normal" being too close to a star, giving you the ability to maneuver and FSD away. It's harder than usual, but possible. It's basically what I tried (and I was able to do before), but in this situation I was unable to turn the ship in any direction. I didn't try FA off, as someone suggested.
What happened here seemed very different from that. Here, first what support stated, then my experience:
Me: "[...] Also, is there actually any way to regularly escape the jet cone? In this situation, my ship was turned 180° towards the white star after reconnect and for the minute until disconnect I was totally unable to navigate towards an escape vector or high wake target."
Support: "[...] Regarding your other query, usually when you're trapped in these situations it means your ship will be destroyed, there are small chances to escape but it's meant to be a risk vs reward type thing. I hope that makes sense.
"
Now to what I've experienced: First, I wasn't very close to the star, I was at the very end of the jet cone (where it becomes dark and cloudy). I supercharged completely and was just on my way out of the cone when FSD failed (which was 100% when I arrived in the system). The computer immediately stated "Alarm, multiple systems failure!", which also never happened before I think.
On my first try to escape, I had the star directly behind me, and it was like I've fallen into a rolling river. I tried to FSD boost, and the escape vector only circled at the rim of the small nav radar. When I was suddenly disconnected (at about 48% hull) and I reconnected, I was turned 180°, looking directly into the sun. Again, I tried to FSD out, same result, boosting didn't help at all. I tried to high wake, but also couldn't align. Again, got disconnected at about 48%. Retried like 5 times, no chance. Apart from the repeated disconnection "bug" (FDEV says they had no other complaints about this), the rest of the situation seems like a random incidence introduced to make supercharging more risky, and it felt quite different to the normal FSD fail when coming too close.
Edit: Wording