The nuts on the back are
flanged thread cutting hex nuts (assuming OEM badge was sourced).
They cut threads into the badge's posts as you tighten down. However, there is also a type of 'plumbers putty' between the nut and the hood skin (since the hood is curved this helps create a flat surface for the nuts without deforming hood). Since the posts are spinning, that's sort of a good thing (though you rightly do not think so at this exact moment) b/c it means the nuts haven't stripped the posts by cutting a groove into them at base.
Bottom line is you need to find a way to grab hold of the post flanges from the top side. Tape up the front area of hood around the post heads w/ some electrical tape (tape an area 3-5x bigger than you think you need just in case). Then use a pair of pincers or lineman pliers to hold the post flanges still while loosening hex nut on the underside. What you can also try to do first is use some needle nose pliers or a screwdriver on the underside and wiggle the nuts and posts a bit trying to crush some of the plumbers putty loose. This will give you a little more to grab onto from the top side. Might also try using a center punch from the underside on the posts but it will be difficult to see it on point due to how small the opening is.
Again, take extra precaution to tape the hood area to prevent scratches (even though the area will be covered by the new badge). Painters tape is so so for this task but I recommend electrical tape b/c it's thicker and will absorb some pressure from tools better (maybe both since electrical tape really only sticks to itself well...)
Good luck