There are a few different ways you can get food.
You can rent a town car instead of taking DME. Most offer a 30 mins grocery stop on the way in.
You can order from WeGoShop. They are basically a personal shopper. You tell them what you want, where you want it from, and they will go buy it for you. They charge a set fee based on the cost of your items, and you pay that, plus the total of the receipt. They will even use your coupons if you have any.
You can order from GardenGrocer. They have a set selection of items on their website. The prices are displayed, so you know exactly what it will cost. However, their prices tend to have some markup over the store, and their selection is limited.
You can order from Amazon. Lots of non-perishables can be ordered from Amazon, with no shipping charge if you buy enough. Just make sure to order it early enough to have it delivered in time. Obviously this won't work for milk and such, but you may save enough on the items they will ship to make up for buying the perishables at the food court/gift store.
Town Car service you do the shopping yourself, just paying for the car service. WeGoShop or Garden Grocer like to deliver to your room, but I believe they will drop it at bell services if you pay via credit card but you get hit with an additional fee so they can tip bell services. Amazon is a wild card due to no guaranteed delivery date with the free shipping (you can always pay for regular shipping).
We used WeGoShop as we found the markups on GardenGrocer to be high. (Had someone local who confirmed prices beforehand) But the delivery charge almost knocked out the savings. Can't say I have read any issues with either. I would suggest to underbuy. It's much easier to run to the food court for a quick snack than it is to justify throwing out food that you never ended up eating.