Can you edit SCCP page files in the HTML Editor for more control over the layout?

Yes. You will need to alter the theme. I have had mixed results with this. I sometimes get corrupt files after altering certain elements.
Find your theme's .sct file.
1. Make a backup copy of it before the next step.
2. Change it's extension to .zip (Right click change name).
3. unzip it to a different location.
4. Now edit this them to your needs.
5. Now zip it back up.
6. Change the extension back to .sct.
7. Import into shop.