"I especially liked the idea of making a sign to show your intentions."
Generally I am carrying a topo map, and the back is white. I just write the word "RIDE" in big letters on it and hold it up.
"If worse comes to worse, we can just go back to the wilderness station and get a permit to take a different trip."
You may find that to be quite a hassle. Maybe not quite so bad if it is mid-week. Still a hassle.
"Also, is there any proper etiquette for hitching a ride? Like, should I offer them money for gas? Do I try and make small talk or just keep to myself? Sorry for sounding like a noob, I just don't have much experience with hitching."
Generally, as you are getting out of the car, you ask if you can chip in a couple of bucks for gas. Some drivers will accept that, and others won't.
I have hitched rides before where the driver went out of his way to drop me off exactly at my destination, and then would not accept my cash. Plus, it was a distance of nearly a hundred miles. The trick was that the driver was going about 20mph above the speed limit the entire way, so I never said a word to distract him.
I hitched a ride in Yosemite one time. The vehicle already had five people in five seats. They crowded up in the back seat in order to make room for me with my pack in the front.