OP, I get where you're coming from. We had a similar issue with both sets of grandparents but not as bad as you're describing. While I agree that it's important to be grateful, I also think it's rude to buy loads of gifts when the recipient has politely asked not to do so.
Our parents have eased off now thank goodness, while in their case it was always done out of love and excitement (first grandchild) our house just doesn't have the room. We did as a pp suggested and asked that they store some toys at their house for when DD visits as we can't physically take any more. Now they usually check with us before they buy anything.