This is one of those “why didn’t I think of that” products. Amazon has this K-Cup Storage drawer for only $14.99. Shipping is free for Amazon Prime members or if you spend $25 on qualifying purchases.
This product is pretty self-explanatory as to how it works, but it is sometimes helpful to read the reviews — it has 4.5 stars from more than 200 reviewers.
Thanks Pink Coupon Cafe!