We have never used Strollers and Groceries, but we have used Kingdom Stroller. Their service and pricing is excellent and the strollers have always been clean and in good working order. I would think the grocery service they have joined up with has similar good service, as they likely would not want to hurt their own reputation. We are out of the stroller stage of our life at this point.
We have used Garden Grocer a few times, and are very happy with their service. They have an app and I can maintain a favorites list, which makes placing an order with them very easy. It looks like the place you are looking at is priced about even with GG. Since you have a coupon (for free delivery, I assume) it may be worth a try. That's a nice savings. FYI, GG offers discounts for 30 and 60 day advanced orders. We go shop is another DIS favorite, but we have never used them. Of course, you would save $$ by stopping on the way to the resort, but you can't beat the convenience of having the groceries delivered!!