Private class member with computed name

Question

With modern javascript we can have private members on classes

  class someClass {
    #privateField = 'foo'
    #privateMethod() { ... }
  }

  const instance = new someClass(); // #privateField and #privateMethod are not accessible on the instance
  someClass.#privateField; // SyntaxError: Private field '#priv' must be declared in an enclosing class

For some time we've been able to have fields with names that are not valid identifiers (e.g. contains spaces, symbols, start with a number, etc.) by using computed values e.g.

  class someClass {
    ["member name that would otherwise be invalid"](){ ... } 
  }

Is it possible to mix the 2 and have private members with computed names?

e.g.

  class someClass {
    ["#private Member with invalid name"]() { ... } // this is not actually private
    #["private Member with invalid name"]() { ... } // this is not valid syntax
  }

I am writing code that generates other code (yes, I am aware of injection risks. Rest assured that I will handle them appropriately). I can be reasonably sure that the members I need to create will not have names that are valid as identifiers, hence I need to use the computed property name syntax. But I also want them to be private members.

There are numerous workarounds I could use including using symbols, mangling or obfuscating the names, or even private-by-convention.

I am hoping for a solution that is more elegant than any of these.