After thinking a bit more about logos in QR codes (the fun never stops!), it occurred to me that instead of obscuring some of the code’s appearance with a logo, you could obscure some of the code’s appearance time with a logo. In other words, make it animated with the logo disappearing or shrinking to some extent and it would still be readable. This has the added of benefit of not needing a high error correction level so you can keep the whole image small.
N.B. If you can’t see it moving please try using a different browser.
At the end of the day, it’s still an animated image which some people find annoying but at least it has a purpose.
I have more ideas but that’s enough excitement for now…