You're right....my spare plate as a backing isn't likely to help on the front much afterall. Still worth considering in other situations if a person needs though.
From looking at your pictures a few thoughts cross my mind. First, the flat stock idea is worth doing if you don't mind doing a bit of fab work. You can also go to a hardware store and look for small angle brackets or other such things....most with holes already drilled out, that might work as well....you just have to measure and size up what you'd need. Otherwise, some other type of fabrication work may be in order too, but you'll have to use your imagination and whatever resources you have available to you.
But trying to stick as close to stock there, you have a few choices. The first two are simple approaches. 1) space out the bottom as you were trying, so as to bring out the bottom enough to keep the overall plate vertical. 2) drill out two more holes where the top was. Since the plate covers over it anyway, looks are only so important here. And if it means saving yourself a ticket fee, it might be worth it. Just put the plate back the way you had it, figure where you'd need to drill the holes and then attach it from the top.
Then there are variations of those. You can do both.....doing the main attaching from the top, but space out the bottom just to reinforce and stabilize it a bit.
My guess is that most of the plate holders you'll find new in stores are going to be flat.....not allowing for spacing out to attach. So you may well have to look for a used plate holder at a junkyard or off another vehicle. I'd be eyeballing every car on the road to look for any possible solutions to this right now. As well as looking through anything and everything in the garage or basement for possible options as well. I had not good holding spot for the plate on the rear bumper from my '76 Honcho that I now have on my '78, so I just drilled two holes on the left side where it'd work and it works well. With the receiver hitch in the center on that a central plate is not a good location. But that's on the rear. Fronts are much better centered. I know the Jeeps often used a plate holder in the front that had an under/behind attachment, and then you bolted the plate to the holder. I'm not sure if those would work for the Eagles....at least without any modifications, but you can certainly look around and consider options.
BTW...I agree on how cheap plates are. I see some states aren't even doing the "raised" element any more...just doing like a straight flat screen print. And as I've mentioned, in Wisconsin, we don't even get two sets of stickers....we only get the rear ones, but still have to use both plates. Anywhere they can cut costs they seem to have done so.
Another thought....if you've got a piece of fairly solid sheet metal around.....size it up, drill two holes that would match the bottom and attach that some how to the current holes (may have to space it out to push it forward as you need), and then four more holes for places for the plate screws to go through. Essentially make your own plate holder in otherwords. Steel would be best there, but if you needed something in a pinch for a few weeks until you got a more permanent solution a half inch or thicker chunk of plywood would probably work as well. Just anything to get the plate sturdy and positioned so you won't get the fine.