Apple - Menu bar icons get hidden by long menu bar items
An app called AccessMenuBarApps allows you to do that by basically providing a keyboard shortcut to an application with no application menu items. It's free, so it wouldn't hurt to give it a try.
I have been using this for a while and it seems to be configurable to do what you need.
http://www.macbartender.com
When holding the command-key you can drag the menu bar items around and change their order. That just helped me when I switched to an app where I could see the required menu bar item and then I moved it far to the right so that I could then see it also in the other app.