Keep in mind that the towncar companies are eager for business. They've been hurt by Magical Express. The towncar companies that will survive are those that are responsive to the needs of their customers.
Don't worry about what a company's website says. Call and ask what it would cost for a 1-way trip with a 20- or 30-minute grocery stop. You night get an answer of "no" -- in which case I would cross that company off my list forever. More likely, you'll get a positive response, though probably at a higher rate than the published 1-way trip without a grocery stop.