As hard as your head looks, I am surprised there wasn't more damage to the Jeep.
That was one of your allotted close calls; it is good that it wasn't worse than it was.
That lick was awful close to your living quarters.
I have had my share.
One experience that made me far more careful happened several years ago.
I had all four wheels of a 24-foot (floor length, 34' overall) Gooseneck all=steel cattle-trailer up on jack-stands and all four wheels off.
I can't remember for sure whether the trailer was connected to a truck or standing on the jack.
I stepped away to get something and
BOOM!!!! , the whole mess hit the ground.
That little escapade learnt me to be far more vigilant in my future doings.
By the way, when you are "learnt" something, it is driven deeply into your skull in such a way that the lesson stays there; being learnt is far more effective than being taught.
I will say this about jack-stands; they are safe support in about 50% of situations, but they are by no means infallible.
Properly placed wood blocks or cribbing are much less likely to topple.
The trouble with any support system is that in most cases the support winds up being right in the way of the work.
As for the working alone as opposed to having a buddy around, from experiences I have had being around most other mechanical afficionadoes, I feel far safer being alone and the more alone the better.
This also holds true for timber cutting, any type of farming activity, and sawmilling.
I can count on one hand the men I don't have to watch like a hawk when I am around them working.
If you need buddies around, make certain that they don't add to the danger.