None of the above suggestions worked. I ended up opening a case with support and after some time, we found a solution to the problem. It seams that when the page is rendered for the Salesforce1 app, there is some code or HTML that is still generated for the header for a standard desktop browser. We were able to correct the scrolling by setting the "showHeader" attribute on the tag to be false. After setting it to false, the scrolling worked and it didn't matter so much if you used an or tag for the page.
I have a test in the controller to determine if the page is being rendered for a web browser on a desktop or in a Salesforce1/app.one application. I use this to either show one form of the page with two columns for a desktop or single column for the Salesforce1/app.one. I use the same variable to set the value for the showHeader attribute so that rendering for the different platforms is automatic.
I hope this helps someone else save weeks of trying to figure out what to do. There will be a Knowlegebase article on Salesforce.com soon.