DME will NOT stop at a grocery store. Not unless coincidentally the bus breaks down in front of a supermarket.
The three popular grocery delivery services are definitely worthwhile, but YOUR question is, is $74.20 spent on just the rental of a fridge, not to mention the additional cost of the perishable groceries themselves, worth it to you?
If you just want, say, some milk for the kids, you can accomplish that with buying s small container of milk or two at your resort, and keeping it on ice in your room's ice bucket.
You may also consider packing some non-perishable groceries in your suitcase. An added advantage of this strategy is it leaves space in your luggage for souvenirs on the way back home.