Chicago Style with BibTeX

Question

I'm using Zotero Better BibTeX to automatically import the bibliography I need, but it uses BibLaTeX and BibTeX, and I am required to use Chicago style. I think

\usepackage[backend=biber,style=chicago-authordate,natbib=true]{biblatex}

would be perfect. However, I'm having trouble to convert to biber.

When I use biber as a backend, following lockstep's advice, i.e. LaTeX Biber LaTeX, I get no errors, but the in-text citations are the automated keys Zotero generates: author_firsttitleword_date. If I rerun LaTeX, I get a lot of "undefined control sequence \entry" and "\endentry", and the logfile is the following monster:

! Use of \sortlist doesn't match its definition.
l.21   \sortlist{
             nty}{nty}
If you say, e.g., `\def\a1{...}', then you must always
put `1' after `\a', since control sequence names are
made up of letters only. The macro here has not been
followed by the required stuff, so I'm ignoring it.
! Extra }, or forgotten \endgroup.
l.21   \sortlist{nty}
                 {nty}
I've deleted a group-closing symbol because it seems to be
spurious, as in $x}$'. But perhaps the } is legitimate and you forgot something else, as in\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.
! Undefined control sequence.
\entry ...ata@\the \c@refsection @\blx@slist@name 
                                             @\abx@field@entrykey 
}\csu...
l.22     \entry{__2004}{article}{}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., \hobx'), typeI' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.
! Undefined control sequence.
<argument> ...equal \expandafter {\blx@slist@type
                                              }{entry} {\listcsxadd {blx...
l.33     \endentry
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., \hobx'), typeI' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

(This is the first time I ask a question, bear with me)

Would programming a new command make sense here? Stick with BibTeX but use a command making the "(Demmer, 2003: 165)" format into "(Demmer 2003: 165)". Is that possible?