To me it sounds like the solution is "We have detected you're using an unsupported browser, iOS does not allow websites to properly access device orientation and therefore this app cannot function"
I wish I had come to that conclusion a week ago, but I'm in too deep now. It's for a little side project, and it seems like the majority of people I want to show it to have iPhones.
I should have said zenith, not poles. The issues occur when the device is pointed up at the sky or down at the ground.
Edit: Though I would imagine it won't work too well at the poles either!