You can make a second player and use them for the paths, that way you can have all the design spaces to yourself without having to use them up with paths
I store all my path designs (I only use mine :3) on my 4th character and dress her in in-game outfits so my other 3 characters have room for clothing designs ^~^
Using four characters you can store 40 designs + town flag + 4 museum designs + 288 saved designs but unfortunately you can only have 40 designs total in your town at any given time, unless you include the town flag.
I'm not sure what the deal is with design signs and face cutouts but I assume they rely on your character's designs too rather than having their own storage spot such as the town flag.
There's no way of having more QR codes in your pockets unless you make another character, QR codes go when you put a design in it's place because you are essentially deleting that design, by replacing it. So therefore it won't be in your list of QR codes, however i'm not entirely sure but I think with the town flag it doesn't change even if you do replace the QR code for it, although don't quote me on it.
Sailorcrossing is right. If you delete the QR of the current flag, it won't change. The same goes for design signs, and possibly cutout stands. So yeah, the most unique designs you can have at any given time is 40.