On BoardGameGeek I stumbled across cajon bags. Cajon are boxy percussion instruments. For a seeingly simple instrument, it can function as a small drum set.
A typical cajon size is about 12" × 12" × 20". Or as I like to think of it, a bit taller than 6.6 copies of Small World stacked on top of each other. And they make padded bags sized to hold cajons.
I purchased this bag, the ChromaCast CC-CBAG-S, in the Standard size. (The Large size probably works, but is a bit deeper, so typical board game boxes might slide around.)
As a board game bag it's nearly ideal. It holds a pile of games. The front zips open, making it easy to display what games you've brought and to slide a single game out or back in. It's got a top; while probably not waterproof, it should protect your games from a bit of rain during the dash from car to house. It's lightly padded, helping protect the game boxes from minor dents. It has a large, comfortable, rubber-like handle at top. While it's heavy when full, it wasn't too bad. It has shoulder straps so you can wear it like a backpack. There it stumbles a bit: the traps are a bit thin, and slinging it on and off my back is awkward. But it's nice to have the option.
The construction seems solid, like a mid-range backpack. The zippers are unbranded, but don't seem flimsy. The sliding parts of the backpack straps are metal. The straps are sown on, and they're not reinforced, but seem okay. It's not amazing, but I'm comfortable trusting my games to it.
At least At least one Kickstarter that tempted me offered a similar bag. For $129. The ChromaCast bag is just $22. The Game Canopy is nicer, but I'm not sure it's $107 nicer. Oh, and you can get the ChromaCast bag tomorrow; the Game Canopy isn't due out until April, 2017.
The bag is new, so maybe my opinion will change after a few months of use. But for now, I'm quite pleased with it.