Mary's idea of a Gravity Groove box would be OK, except that it could be awfully big for that frame design.*
How about a cabinet frame? You could easiy build something like the one depicted in the "Special Purpose Shadowboxes" article in PFM's November 2009 edition, page 32.
Rather than making one huge frame, suggest making two smaller frames, which would be easier to display and handle. If you allow 3" diameter and 12" height for the bottles, you could build a 2" to 2-1/2" deep shadowbox frame about 30" wide x about 40" high, which should accommodate about 30 bottles (3 rows of 10 bottles). Hinge door-frames on each side. That is, it could open like a cabinet with two "French doors". Depending on your choice of mouldings, the doors could provide up to an additional 2" of depth.
Inside the box, a row of bottles could sit on the bottom, and you could install two horizontal shelves made of acrylic or glass for two more rows. Due to the 30" (or so) length of shelves, you would need to embed them in slots in the reinforced backing board.
If you would like help with the cutting and assemblies, let me know. My shop is only about 20 miles from yours, and you're welcome to stop in any time.
*When I developed the original Gravity Groove design in 1990, I wanted to find the practical limit of size. A guitar-sized Gravity Groove is no problem. The biggest one I built was 48" square, and it worked well...except that removing and replacing the acrylic box-cover required the coordinated effort of two people. And when the cover is off the base frame, the large acrylic box is flimsy and could be broken easily, or scratched. These limitations would apply to Gemini/Showcase Acrylics' "Enhanced Gravity Groove" designs, as well.