Wow! very nicely done. Seems like the thread was placed into good use!
For this design, you are actually meant to place only 1-2 cards per slot (by right..).
Putting more cards into it would mean
- it will bulk up due to the number of cards. which leads to 2 scenarios
-leather will stretch eventually. so u are able to pull in/our cards easier.
-put more cards in.
-it will become a little loose in the future.
Other than that, you should try to use softer leathers. Less in thickness (oz.) and softer in nature (e.g. sheep or goat). Like this, you can put more cards in due to it being more forgiving, since its less stiff.
Its not really due to the stitching (since I don't see 'hills and valley', that's the effect of over-tension). More to do with allowance of space. For this design, its meant for less cards.
So, its more like a nature of the design. That's why card holders you see in commercial products are more towards individual plastic cases for each card design OR a single big compartment to place cards into it.