I bought this 4.5 years ago and it’s still ticking. Might get another couple years out of it.
Alpine Swiss Genuine Leather Super Thin Slim Cash Strap Front Pocket Wallet https://www.amazon.com/dp/B00EOYKEEA/ref=cm_sw_r_cp_api_glt_fabc_240DM6HDXJSWS2ZD0SG2?_encoding=UTF8&psc=1
Different design, but still a pretty slim card holder. I've used one for awhile. ($15, i thought it was $10 - but they have another model that's $12 that holds cards horizontally)
https://www.amazon.com/dp/B00EOYKEEA/ref=cm_sw_r_cp_apa_hSIuxb5HWF84T
I use this Alpine Swiss wallet, and it sounds like it meets your criteria. It's also pretty affordable too, which is nice. https://www.amazon.com/dp/B00EOYKEEA