Javascript indented method chaining

Hmm... With the basic, 'Default' code style scheme, I get your code formatted as:

http.fetch('myStuff', {
  method: 'GET',
})
  .then(response => response.json())
  .then(data => {
    this.stuff = data
  });    

Looks pretty much the same as your desired formatting...

P.S. I'm using 2016.3 EAP

Note that you can exclude certain code fragments from formatting - this can be done by surrounding the regions you don't like to be touched by formatter with the formatter markers, like

//@formatter:off
your code here
//@formatter:on

But you need to make sure to enable these markers in Settings | Editor | Code Style, Enable formatter markers in comments

To my eyes, it looks very different and actually makes it harder for me to visualise scope blocks when writing anything more than very basic code. That little indent to me indicates that the code below is nested within it, when really it's at the same level of scope.

hmm... but your 'Expected format:' example is also indented - the only difference is that yours seems to have 4 spaces indented, and mine is using 2 spaces indentation...

OK, here is the configuration that seems to produce exactly the expected result:

 <codeStyleSettings language="JavaScript">
    <indentOptions>
      <option name="CONTINUATION_INDENT_SIZE" value="2" />
    </indentOptions>
  </codeStyleSettings>

http.fetch('myStuff', {
    method: 'GET',
}).then(response => response.json())
  .then(data => {
      this.stuff = data
  });