How many groceries do you need?
We discovered that we could pack the basics - we don't cook in our room much - so the shelf stable stuff gets packed (you can ship it as well). For us thats cereal, laundry detergent, sugar, coffee, salt and pepper, cereal, snacks, peanut butter, etc.
When we arrive we stop at the resort shop and pay the resort prices to get milk, bread, half and half, cheese and eggs.
This won't work if you required non-shelf stable foods that aren't carried at the Disney shops.