Chris, if your choice gems do not fit tight enough, you can do something about it. It will require a bit of time, careful measuring, and a small amount of money.
Here we go. Go to HOBBY LOBBY. In the back of the store they stock their Crescent Matt Boards. These hefty cardboards are a good 1/16" thick. You could carefully measure the inside of your glass case (but allow a bit of room as clearance, draw your lines, and cut with a utility knife. Add as many as needed beneath your current pad, and viola, that should provide plenty of extra height to secure your gems in place when you close the lid. BUT DO NOT ADD TOO MANY, AS TOO MUCH PRESSURE ON THE GLASS LID COULD CRACK IT IN TIME!
If you want to fashion your own pad, go to a fabric store and purchase a few yards of their highest quality or mid-quality white cotton batting (sp?). Using the crescent board as a base, make as many layers of batting as you wish, gluing them one at a time with something like Elmer's spray glue. Always make each batting piece over-sized so it will be easy to attach. Then trim the excess batting with good scissors. Also, don't go crazy with the spray glue. You don't need a lot to attach the batting. Now, you may wish for a sturdier pad. Simply make your base thicker by gluing as many of the crescent boards together. I would stop at 3, but that's up to thee. To crown your pad, Hobby Lobby stocks some quality velour that looks and feels terrific. They have an assortment of colors, including a nice red, though you may wish to employ their slightly darker red, which is almost a maroon. Their green is nice and dark. The midnight blue is my personal favorite. Or, you could do the same thing with crushed velvet, which comes in other colors. When you cut the velour, allow an extra 1 - 1 1/2" of room all the way around. As always, allow 30 minutes for the glue to reasonably dry, perhaps longer, and then fold over and secure the velour flap on the back with good gray duct tape. That's right----duct tape. Or you can cut each corner at a 45-degree angle and then your board will lay a bit better. Just don't cut too close to the corner; leave a quarter-inch buffer. When attaching, it stretches nicely and gives the board a smoother and more professional appearance.
In time you may want to go with a 37" X 22" All-State case. Expensive, but think of it this way. You spent a lot of time and money on those gems. Allow yourself the luxury of viewing them in a quality presentation. Honestly, I think you will discover it's well worth some of your "card" money.
Naturally, I want to express to you: Nice collection you have there! -Brian Powell