I have a lot more confidence in my 40mm Giant Crosscuts keeping me attached to the road then I did on my high pressure tires on my hybrid. 50psi with me at 192 lbs and they are pretty grippy. Not sure bigger knobs would make a difference in that situation that dumped you.
I like throwing the bike around, but am always concious of my age and have a fear of falling and breaking into pieces which tends to make me a bit cautious.. I think if I was with you on that ride and we hit that turn at speed I would of dumped too.
Anyhow, TimothyH had posted a sale on those Gravelking SK's the other day and I almost jumped on them. But my tires are good for the rest of this year. Wish someone who rides with SK's would answer your question about them.