static constexpr member of same type as class being defined

If I interpret the Standard correctly, it isn't possible.

(§9.4.2/3) [...] A static data member of literal type can be declared in the class definition with the constexpr specifier; if so, its declaration shall specify a brace-or-equal-initializer in which every initializer-clause that is an assignment-expression is a constant expression. [...]

From the above (along with the fact that there is no separate statement about non-literal types in static data member declarations), I believe it follows that a static data member that is constexpr must be a literal type (as defined in §3.9/10), and it must have its definition included in the declaration. The latter condition could be satisfied by using the following code:

struct Foo {
  constexpr Foo() {}
  static constexpr Foo f {};
};

which is similar to your Attempt 1, but without the class-external definition.

However, since Foo is incomplete at the time of declaration/definition of the static member, the compiler can't check whether it is a literal type (as defined in §3.9/10), so it rejects the code.

Note that there is this post-C++-11 document (N3308) which discusses various problems of the current definition of constexpr in the Standard, and makes suggestions for amendments. Specifically, the "Proposed Wording" section suggests an amendment of §3.9/10 that implies the inclusion of incomplete types as one kind of literal type. If that amendment was to be accepted into a future version of the Standard, your problem would be solved.

I believe GCC is incorrect to reject your Attempt 3. There is no rule in the C++11 standard (or any of its accepted defect reports) which says that a redeclaration of a variable must be constexpr iff the prior declaration was. The closest the standard comes to that rule is in [dcl.constexpr](7.1.5)/1_:

If any declaration of a function or function template has constexpr specifier, then all its declarations shall contain the constexpr specifier.

Clang's implementation of constexpr accepts your Attempt 3.