You could also do it the menial way; create multiple QR codes that can connect together. Not very practical for everyone except the very-motivated.

Why not record with a standard high quality webcam and do the QR processing later? That’s how I would exfiltrate a large volume of data.

I've done a POC with the native QR reading code on iOS. The short answer is: it's not a problem at all, and you can drive very large QR codes for more efficient transfer.