Joe:
> One of the main things about the 2BE construction is that it
> constitutes an equational sentence. Normally, however, equational
> sentences are reversible:
>
> - George W. is the president.
> - The president is George W.
>
> This is not the case with 2BE:
>
> - The thing is, is that we don't know how to analyze this structure.
> - * That we don't know how to analyze this structure is, is the thing.

Also:

  I don't know where he put it, is the problem.
 *I don't know where he put it IS, the problem.
 *I don't know where he put it IS, is the problem.

> The reason why 2BE is not reversible has to do with information
> structure, I think. The subordinate clause must belong to the rheme
> (comment) and, unsurprisingly, the initial focus NP (e.g., formula
> phrases such as "the thing," etc.) must marked as thematic (i.e.,
> it must belong to the topic).

Are we sure there is a rule of reversibility as such? It could simply
be that the range of things that can be complement of (equational) BE 
pretty much overlaps with the range of things that can be subject of
BE, without there being any rule that says 

   "if a word of type X can be subject of BE then a word of type X can 
   be complement of BE (and/or vice versa)"

In the case of 2BE, the grammar would include a rule that allows the
clause ending in BE1 to be subject of BE2, but no equivalent rule that
allows it to be complement of BE2.

A pair like

1a   Go home is what I want most to do.
1b   What I want most to do is go home.

superficially seems to demand a rule of reversibility, for it would be
a strange coincidence if bare infinitives could exceptionally be
both subject and complement of BE in just this construction. However,
on the basis of 1 minute's thought (so what I'm about to say is probably
wrong, & I'm conscious of there being a literature on the complexities
of this topic, which I've never got round to consulting), it seems to
me as though what's going on is the following.

2a   Is (to) go home what you want most to do now?
2b   Is [what you want most to do now] *(to) go home?

This seems to show that a bare infinitive can be an invertible subject
of BE but cannot be complement of BE. Hence while (1a) is 
straightforwardly Subj+BE+Comp, (1b) should be seen as 
Extracted-comp + BE + inverted-subj.

--And.