Gothitelle unfortunately has nothing it can do that isn't done better by Mew. for CM, it has better speed, bulk (both sides), Special Attack, a healing move, and the threat of physical or stall breaking sets to lend to unpredictability. It also gets Dark Pulse, but neither are doing jack shit to chansey with it so it's kind of a moot point.
It also has all of the support moves you listed (block over mean look), and Will-o-Wisp to outclass Tickle or Charm.
Synchronize is also better than Frisk on a set where status is a big bummer.
Sorry to crap all over this idea, it's just that the QC and GP teams have a big job assembling the strategy pokedex and they don't need to do analyses for NU material pokes unless they really have something to offer overthe other options.
I know you've done a lot of work for the process so far and I hope you realize I don't mean this personally. Still it is what it is, and in this case it's a pokemon who basically has nothing but Frisk to differentiate itself from, let alone gain advantage over, one of the top threats in the metagame.
It may be a different story if Mew goes to BL, but for now that seems unlikely.