What Does SPQR Stand For?

The abbreviation SPQR means, in English, the Senate and the Roman people, but what exactly those four letters stand for -- in Latin -- is a little less clear. My take, which I've recently changed, is that SPQR stands for the first letters of the following words with "-que" added as the third:

Senatus Populusque Romanus.

That -que is added to another word doesn't mean it wouldn't be heard as a separate unit of meaning. Many think the letters stand for Senatus PopulusQue Romanorum, which is what I thought until I realized that that would be redundant -- translating as it would as "the senate and the people of the Roman people". There are other variants, including Romae, instead of Romanus or Romanorum. The Romae could be a locative or a genitive. There is even a suggestion that the Q stands for Quirites in some form.
It seems likely that Romans used SPQR to stand for more than one of these options. What is your opinion? Do you have any evidence? Do you know of any uses of the abbreviation before the imperial period? Please post in this SPQR forum thread.