For clarification: yes, it is the west > east bisection of the hook as opposed to core punching from the north.
how is it executed properly and safely, and have you ever found yourself in extreme danger because of it?
It isn't executed safely, and you're in danger every time you do it. I've done it on Mapleton, Langley, Wayne, Wakita and a few other large tornadoes, and a handful of smaller ones. I do it much less frequently in the last year or two, because I like returning home to my family alive.
Pros:
-It's an efficient way to get very close to a tornado, and opens up another avenue for attack especially if the road network made SE positioning troublesome.
-Very, very rare for a tornado to loop back and travel west, so as long as you don't cross in front of the tornado, the chance of getting directly hit by the tornado is small.
Cons:
-Not crossing in front of the tornado isn't as easy as it sounds
-TWISTEX did it at El Reno, pretty good example of why not to do it. In fact, Tim seemed to prefer hook slicing and the only times I ever saw him chasing was when we were both in the hook. It was likely the easiest way to get directly in the path to place probes
-You're in extreme danger every time you do it, because you're bisecting the bear's cage and aiming right for the bear
-Your escape routes can be limited simply by the storm changing, and no two storms will act the same. "Drive south" doesn't work. I've had to escape north, south, and west before.
-You almost need a partner looking above the car and watching rain/wind patterns around you
-You follow in the debris path meaning that your roads may be blocked, and you're much more likely to come across injuries and deaths
-There's a good chance of driving over wood with nails sticking out
-RFD driven hail can easily take your windows. Wakita was lobbing softballs sideways with 75mph RFD.
-The tornado is moving away from you and your precip-free window is 1 minute tops. No time for tripods or enjoying the storm.
-Rear inflow jets like to take your back window out, especially if you're in a vehicle with more vertical window profiles like an SUV
It's actually easier to do the larger the tornado is. Even on HP storms, there seems to be a ~1/2 mile precip free zone directly around the tornado where hydrometeors are shunted away. I've never been surprised by a large tornado while hook slicing, but the smaller ones (EF0-EF2) can almost come out of nowhere.
The most important part of safety is not ending up in the tornado's path. To do that in heavy precip you have to know your position relative to the updraft, and watch the rain/wind patterns. This isn't something that can really be taught or explained, it's experience gathered from being close to tornadoes. RFD/inflow transitions, inflow jets/the "ghost train" - they're all things that you have to know intimately and watch for. It's easily the most stressful thing I've done while chasing.
As such, the hook slice shouldn't be attempted by anyone without that experience, and probably shouldn't be attempted at all. Especially as this thread is in the intro section. I'm not trying to be elitist or anything, but unless you've been close to more than a handful of tornadoes, hook slicing can be a really bad idea, and even for veterans, it's a risky maneuver.