... somehow it comes across as emotionally threatening instead of welcoming...
+1
Along my idea that once one conquers the HOW of post-processing, the most important thing becomes the WHY. We tend to get enamored with a technique, especially if new and popular, to the point that we forget why we are doing it. We bring out shadows (or details, or whatever) because we can, not because we should.
We also tend to apply tricks and techniques indiscriminately, across the image (hence my distaste for packaged solutions, the likes of Nik suite - they ultimately look like a canned laughter). Even when applied with a local brush, we tend to choose the wrong location: we open or block shadows where we shouldn't, esthetically speaking.
Btw, the above is not intended as a criticism aimed at David in particular... we've all been there, done that.
In particular, in the OP photo, I find the right side of the sky acceptable, but the left side, around the sun, appears to have exacerbated whatever tint was there, to the point that it becomes objectionably purplish/cyanish.
On a general note, when pulling things out of a shadow, we should bear in mind that things there can not possibly be as contrasty as the rest of scene (probably the cause of the "emotionally threatening" impression).
Compositionally, the tree and sun are too far to the left. No cropping or zooming would help, but simply walking around. Hiding the sun further behind a branch would have helped tremendously with exposure as well.
Exposing ETTR would not help either, because you are already burning the area around the sun. The only thing that would have helped is to bracket.
Also, processing the same raw file twice (once for shadows, the other for highlights) and then combining them for a HDR does not normally work, as there is no new information in either file (if I remember correctly, earlier PS versions would warn you so and refuse to blend it).
Also, as David discovered, just saving a single file as a 32-bit is not going to add any new information.
