You need to call those you would like to try. No car service offers one-way transportation with a grocery stop online. Most of them will take care of you if you call them and tell them what you need.
And here is the issue. The vast majority of people are going to check out websites and then, based on what they see there, choose a service. If a grocery stop isn't offered, they will go on to the next one on the list. Why, in heaven's name, would the normal, everyday person, think that if they call and speak to a person, they will get a different answer??
I have had a slightly different experience. I booked our towncar service for our Thanksgiving Day arrival. I wanted to stop and pick up some light snacks and drinks..not a grocery stop, just a convenience store. Our flight arrived, ontime, just before noontime..maybe 11:30-ish. Well, our driver informed us that since it was T-Day, there weren't any stores open, so we wouldn't be able to stop. I told him that I had specifically asked about a grocery stop when I called and booked our ride. I had been told that there would be a store available. This guy said 'Nope, they all close before noontime. Sorry.' and kept on driving.
I wasn't happy to say the least. We all know that there are convenience stores open on holidays...everywhere. I was sure to email the company when I got home to let them know of my disappointment in the service given. And that was round trip....I was more than entitled to the stop.
SO...I guess I'm asking why someone would feel the need to call in person to see if the policy on the website is 'really' real. I don't think that's the best idea or way to do business. But, that's just me.