Aside from CORI having very few shops available in my area in the last month or so, I have been leary of taking shops from them because of issues like this posted about their upgrade issues. I did do two when they got high enough, and was lucky that my reports were accepted. Like the OP, I also keep copies of the confirmation page and my report!
I almost always use Google Chrome for my CORI reports (and everything else) and only a couple of times has it been an issue. Those times, I just copied/pasted my answers using IE. (I hate IE!)
In the OP's situation, CORI's response is thoroughly asinine. It makes me livid when complete morons are in charge of my fate, and refuse to see/accept reality and the truth, and make things right as any normal, rational, human being would. Good Lord!
I hope everything works out... I would recommend a phone call, too ~ ASAP!
Practitioner of the Nerdly Arts.