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I was thinking about 3 M double sided tape (gray - medium hold) just to hold it in place against the nosecone. If you measure the metal hook right, the plate bracket should be flush with the cone. Just a matter of holding it in place, or, as you put, put some foam tape or other means to not damage the cone.
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By the way, the hook is supposed to be one of two, for each side (end) of the plate bracket. I didn't want it to look like it's only one piece holding the bracket.
Only problem I see with that is that the nut that goes over the front end of the j hook will be in the way of the license plate being flush and vertical.
But it's pretty much the same concept, just without the vertical extension of mine.
I'll finish it this weekend and let you know how it went.