Jeff,
I have been following this post and finally decided to jump in and offer some insight here.
First of all, Jarvis is correct with the 38N hinge he shows on the Amazon link. This will give you the ½ overlay and soft close. You could also go to a local cabinet shop and ask them to order the hinges from the local Salice or Blum wholesaler.
Secondly, the brand name hinges of this type (Salice, Blum) will have the overlay stamped in the hinge arm (i.e. ½, Ύ, 1, etc
). This will verify that you have the correct overlay. I am not sure if the Home Depot Chinese hinges have this identifying stamp.
Next, all one piece face frame hinge brands bump the door out away from the face frame about 3/16 to Ό. This is a natural characteristic of this hinge type.
Third, the photo does show a one piece, compact style. This style hinge does not require a hinge mounting plate. They are one piece and there are many depending on the overlay.
Also, I find the photo to be a little unclear. It seems you may be actually holding the hinge up to the style incorrectly.
Here is some information that may be helpful.
Best of luck.