Well I don't have one of those trucks. We have all have had plenty of rusted bolts and screws that just will not come off. I have used all kinds of methods. I don't like the drill the head method but I do it sometimes. You keep talking about going to a shop. If you have money for that, just buy some tools. You can't keep going to a shop for this mundane typical restoration stuff. They will charge a lot for that job. I offer some observations, experience and suggestions to ponder and build upon. I love this kind of problem but it's hard to come up with a good suggestion when I can't see the back side of hood. I've looked at used emblems for sale on Ebay to get an idea of its structure and mounting.
1. Get a 4 1/2" electric angle grinder. Kevin's suggestion. Too bad you can't get a compressor and a die grinder. That would be the best tool. Smaller but powerful.
2. Get some goggles and gloves.
3. Get brave.
4. It seems like pictures I see show that the emblem has threads and the screw must go thru a bracket into the emblem threads from behind. Instead of drilling head, I usually cut a cross in it with a die grinder and just kiss the part that the head is against. Center of cross is center of screw head. Then a small chisel and a small hammer will snap off the four sections. This leaves me maximum shank to grab for the slow back and forth after PB Blaster soak if I'm saving the female threads. In your case you are not trying to save any threads if I see this correctly. If you can not access the screw heads holding the emblem on, see 4a or equivalent.
4a. Attack from the front side leaving four 1" squares or the "clips" at screw attachments. Most of emblem will be gone at that point and visual and tool access will be enhanced. Then proceed to cut off the squares and cut off the shank/clips and withdraw screw from rear.
The 4 1/2" angle grinder is a manly tool, high speed, very sparky and dangerous if you do not take control of it with conviction. It's also fun to blast everything that won't come loose. Just don't cut the hood in half. Don't spark near gas or glass or flammables or people. I recomended the angle grinder because you said you have no air and you need something that will work at a reasonable price. I have a Harbor Freight one and a Ridgid one. Use a 1/16 thick cut off disc for this. When you use it to actually grind something, you will use a thick disc.
If I don't see this emblem attachment properly, please someone correct me....or supplement my brainstorming.
No offence to Dusty but the video is not even close to what we are taking about when drilling a head off as Kevin said. Note to Kevin: Why are you needing to hold the head with vice grips? If it spins, it breaks off or the whole screw is tightening? If the screw is not threaded into threads on the emblem, my question is moot.
No offence to Brad but I have never found a dremel to be robust enough for this kind of job and the "bits" wear out too fast.