So after multiple heartbreaks about where to store my wine, I'm happy to say mission accomplished!
I found this wine rack at Crate & Barrel's online outlet. The wine rack is 13x13, which is the exact inside dimensions of Ikea's Expedit shelf. Let me just say, one of these stores is lying about their size, because the wine rack was about 2 cm too big.
After giving Brent enough sad faces, he went to the garage and put his new saw to good use.
Once the perfect fit was guaranteed, the painting began. I'm really happy with how it turned out.