Besides, wasn't the original film basically a Star Trek farce?
People always say that, and there was indeed a lot of Trek in the mix, but it was actually riffing on a lot of SFTV.
Galaxy Quest was an early '80s show in-universe, so that puts it in the generation of
Battlestar Galactica and
Buck Rogers in the 25th Century. Alexander Dane owed as much to Barry Morse from
Space: 1999 as he did to Nimoy, and I always thought that the "warrior alien" Dr. Lazarus reminded me of Hawk from
Buck Rogers. The token character whose job is basically to repeat what the computer says is reminiscent of David Kano from
Space: 1999, and a female officer who's just there to look pretty is as much like Athena from
Galactica as Uhura. The precocious kid Laredo as part of the crew is evocative of Will from
Lost in Space or -- uggghhh -- Doctor Zee from
Galactica 1980. The cheesy wire-and-puppet effects suggest the Irwin Allen shows or maybe
Space: 1999 (though its wirework spaceship scenes were mostly superb). The bit with the random deathtraps in the ship's corridor is just a nod to action shows in general, maybe a bit of Irwin Allen or
Doctor Who or the Glen Larson shows.