Is there a way to make EmEditor move through document tabs in sequential order from left to right?
Yes. Go to Tools | Customize…, then select the Window page, and clear the Switch to Last Used Document for Next Document Command check box in the Options list. When unchecked, you can switch between the tabbed documents in order from left to right, or right to left, using Ctrl+Tab, or Ctrl+Shift+Tab respectively. When checked, pressing Ctrl+Tab and Ctrl+Shift+Tab will switch back and forth between the active document and the last viewed document.