You really can't (safely and conveniently) walk to the MK Hess station. We always use Garden Grocer. We find paying a bit more for groceries than we would at home is well worth it in terms of the time and effort it saves us while on vacation.
And if you are doing a split stay, bell services can transfer the refrigerated items between resorts as well. I don't think I would risk frozen items, but for refrigerated ones we have never had a problem with them getting moved and staying cool.