That '70s Trek
Captain Eric T. Forman
Science Officer Hyde
Dr. Kelso
Helmsman Fez
Communications Officer Jackie
Yeoman Pinciotti
Chief Engineer Red
Voice of the Enterprise Computer: Kitty
Orion slave girl: Midge
Away Team Red Shirt: Bob
Yours is good, but you reminded me of something!
There was a one panel cartoon in an old Starlog magazine issue, about the time of ST:TMP where they had almost this same thing. Except Daffy was Bones, Bugs was Spock (he already has the ears), Elmer was the captain, Porky was Scotty (“I’m having trouble with the di-di-di…uh, no power, captain!”) the road runner was Uhura, and the Klingon adversary was Kosemite Kham. They all had dialog panels that fit both the 'toon characters and the ST characters. It worked really well.
Dr. Kelso? :eek: Would Yeoman Pinciotti have the Janice Rand hair but in red? And the skirt? Ohhh, baby. You win HUGE points for Computer Kitty–I can hear that laff every time they make access Explosive decompression in 15 seconds–Ha, ha, ha!!. Blond hair/green skin Midge might just work.
Randy needs to be a red shirt.
What about Leo? 
It’s…
Monty Python’s Flying Starship (cue the Star Trek theme re-imagined as a Sousa march)
Capt. Graham Chapman (doing the commander bit)
First officer Eric Idle
Ship’s doctor John Cleese (frustrated: “I’m a doctor!” under his breath “…not a bleeding bouzouki player.”)
Communications officer Terry Jones (in drag, of course)
Engineering officer Michael Palin (as a Gumby)
Navigator or Helmsman Terry Gilliam (since he’s the resident foreigner)
Badly mis-cast TNG
Captain Wesley
First Officer-Troi
Ships Counselor Lt. Worf
Tactical Officer Guinan
Ensign “Mid-Life Crisis” Picard
Ship’s Doctor Geordie " I Can See Though Clothes" LaForge
Transporter Chief-Lt. Barkley
10-Forward-Occasional shot of Riker on trombone
10-Forward manager-B. Crusher
Comic relief-Data
Space hippie.
Leo could be Q. Or Harry Mudd. Or a star fleet Admiral. Or the guy selling tribbles. Or a Romulan.