Well I figured it out.
The Raleigh badge I had was installed using a couple holes in the head tube. The badge had a couple posts on it that they pushed into the holes and then smushed so they couldn't pull back out. All I had to do was pop the ends off and the badge fell off.
1. First thing you have to do is take the fork out of the head tube. This means the handlebars are coming off and you have to loosen the nut that holds the fork's bearings together. I'm assuming you have the wherewithal to handle this step, so I'll cut to the chase.
2. Once you have access to the inside of the head tube, look down inside there and see what's going on. If you don't see any holes or protrusions coming from the badge side, chances are the badge was just glued on. If this is the case, this how-to won't help you. You're just going to have to grab a razor and attempt to carefully cut the glue/patch off of the tube. Good luck!
3. If you DO see little bumps, go grab yourself a clean sharp flathead screwdriver OR a chisel. It's just soft aluminum, so it shouldn't do any damage to your chisel if you're careful with it.
4. Place your device of choice against the post and knock it off with a sharp tap with a hammer. This will take a few tries, but you'll get it. Just be careful not to gouge too much out of your frame. You just need the end of the little post to fall off, so it shouldn't take much force at all.
5. Once you have them off, it will be ready to fall out, but you may not know it. If you feel like you took a little material off the posts, use a flathead screwdriver to push on the post to push it out. You'll have to use a little leverage against the top of the tube, so grab a piece of wood or a rag. You don't want to put any force on the tube or you'll bend/dent it.
6. After a little finagling, you'll get that thing pushed out and the badge will fall off! Tadaaa!
Now be CAREFUL with it because it's fragile and if you bend it it'll never fit well on your tube again. Go place it somewhere safe and get going on that paint job. I suggest Citristrip to get the paint off. It's WAY better for the environment than aircraft stripper and it's way easier to use. Just paint it on (gloves and goggles) and wait a day. Take it off, then do it again on any spots that didn't come all the way off.
And yes, I made this @ TECHSHOP!