We've gone through the same (first world) problem and are currently experimenting with the following method - Our child is allowed to open all gift wrapping. A

We've gone through the same (first world) problem and are currently experimenting with the following method - Our child is allowed to open all gift wrapping. All underage/overage gifts are kept separately. Out of the ones for his level, he's only allowed to open one per day. This also only happens in exchange for removing one toy from this current set to give away for donation. There are two outcomes we expect:(1) Toy stash volume is kept constant and (2) Child decides which one to keep. It worked well at Christmas; let's see how the birthday goes...