Hi Craig!
Sorry to hear that you’ve hit a roadblock here.
The reason you're not able to play your course locally in Internet Explorer and Microsoft Edge is because those browsers block local playback of Rise courses (unlike Google Chrome, Firefox, and Safari). That's why you're just seeing a blank page in these browsers. To use Internet Explorer or Microsoft Edge, you'll need to upload your course to a web server. Here's an article that talks about how to do that.
It's my understanding that SharePoint Online (the Microsoft Office 365 Hosted Edition) won't play HTML files. As a result, SharePoint Online can't host published Rise content, which includes HTML files.
You should be able to upload Rise content to a SharePoint Server you host, and you'll want to check with your SharePoint administrator for instructions on how to host HTML content. Depending on your version of SharePoint, you may need to switch to explorer view before uploading content, or you may need to check in content after uploading it. Your administrator will know for sure.
If you need to track learners' progress and results, publish your Rise content for LMS and use SharePoint's free Learning Kit.
I hope that helps! :) Let me know if you have any other questions.