Interesting product, and one could manufacture something similar in a few minutes at home without trimming the key ring sized cards with a photo pocket (from the set that comes with most wallets) and some strong thread, but I have a few other ideas.
Only carry the cards you actually use.
If that's still too many, carry only those you use at least once a month. The others can be kept at home and brought along on shopping trips when needed. (We have a few that we use often enough to keep, but not to carry -like pet supply and video store cards- so they live on the bulletin board over my desk, tucked in the bottom edge. We just grab them on our way out if we plan on using them.)
If you don't want to pare them down, pull them off the key ring and give them their own. Then you can chose to carry the cards (or at least the grocery store ones) inside your coupon holder. Or store the card ring in the car so the cards are always handy if you chose where to shop at the last minute. Or keep the card ring in a specific pocket of your handbag if you carry one.
A few years ago, I moved mine to a separate keyring to cut down on things I had to fumble with when I needed my keys. Last year, I pared my cards down when I discovered I had three cards I hadn't used in over a year. (Here's the part where all the women here will think I'm nuts.) Then I decided to stop carrying a purse unless absolutely necessary. I've always carried minimal baggage, and I spend most of my time in jeans, so I decided to make use of my pockets. I now carry lip balm, a hair tie, and my very few must-have keys on a simple ring in a front pocket, and a flat rectangular zippered change purse in a back pocket. The change purse is just barely big enough to hold my necessities: A few cards (ID, 1 debit/ATM, 1 credit), cash (bills folded in half separately for easy removal), a slip of paper with emergency numbers, and the key ring sized versions of my loyalty/club cards (there are only 4 I use often enough to carry). I have to be prompt about keeping my receipts and loose change cleaned out of the "mini-wallet" to keep it usable, but traveling light is worth it. No purse, no ugly bulky pockets, no frills. Simple, organized, and clutter-free.
One last note, and this is grocery store card specific: My fiance and I do a lot of our grocery shopping together, so with the exception of our favorite grocer, we don't carry duplicate supermarket cards. In other words, we both carry store A's card, but I have B and he has C. One less card for each of us to tow around. We don't visit B or C more than once or twice a month, so it's not a big deal to plan for the card carrier to go (or hand off the card) when we do.