Your Solution 3 can be shorter:

f(\[]);
[download]

or even

f(\{});
[download]

Whether it is elegant is in the eye of the beholder. It surprised me that this worked, since the scalar is a reference to a reference, but it can be assigned to and modified, unlike f(\1) which gives a reference but is read-only (but does appear to return different addresses each time called).

Update: The following also appears to work in this case

f(\());
[download]

but this is an aberation of the subroutine call interface.

my $ref = \();
$$ref = 42;
[download]

Gives: Modification of a read-only value attempted