As much as I love this movie, I NEVER considered it an influence on Reckstar... until I heard an interview with John Carpenter in which he describes the movie's protagonist as, "Kurt Russell thinking he's a hero and not realizing he's a sidekick." That's almost my entire pitch for Reckstar... so, I guess Big Trouble is an influence!
Part of the RECKSTAR mission statement was to pull influence from every form of space or planetary adventure, and this is the grandaddy of them all. It's no coincidence Finn brings a sword to his laser gun fight.
Like Firefly/Serenity, Bebop's influence is mostly about the crew dynamics, and how two scoundrels manage to build a family around them. Also, one of the planets Finn & Thade visit later in the story was inspired by something from Bebop. See if you can figure out which.
I felt like I was in a race to get RECKSTAR going before this movie was released. Considering it's about a group of misfits (including a couple green aliens and their immature, blond-haired leader) on a music-infused comedy-adventure through a melting pot galaxy... you can probably guess why.