[whpalmer4]

Not aware of a way to get the behavior you request for the tab drawer, but a workaround you could try would be to minimize the width of the tab drawer. You can slim it down to about 2x the width of the little gear menu at the top of the drawer.

You can control the user agent used for a given site/domain via the site specific preferences. See OmniWeb→Show Site Preferences, Preferences for <domain>, Other tab.