I happen to be "working" on a CardBoard based terminal emulator to do my programming while on the road. During initial development of the Fairphone we increased the DPI settings to match the physical DPI settings on the screen and (by chance) the Cardboard was also working properly. This however broke the tests executed by the google test framework that require the DPI settings to be chosen from a predefined list of DPI settings. We reverted the changes and there is not much we can do. I therefore think that the solution is indeed to play around with QR codes.
Personally I preferred the higher DPI settings more but this is a no-go for google compatibility
My emulator(only a few lines of code currently) is based on termux (a quite complete unix environment for your phone that include things like vim,tmux , clang etc). Installation does not require root
if you wonder what it looks like ->