Burnt Truck from Orange County has some of the best sliders in my opinion. They only do sliders.
A few of their sliders include the Fried Chicken Slider, Cheeseburger, Sloppy Joe, Pork Belly, Spam and Egg slider, Meatball, PB&J, Vietnamese Pork, and a bunch more on rotation.
Check them out on Yelp.
First suggestion would be, contact your favorite food truck and find out whether they can arrange this.
After that, look for a truck that strikes your fancy on FindLAFoodTrucks.com and see what they have to say. You'll most likely have to contact them via Twitter.
Good Luck Bar
1514 Hillhurst Ave, Los Angeles, CA 90027