Instead of cluttering the top of every page with several contact links, it may be easier to provide a single link to a contact page using the standard announcement bar. On the contact page you can then provide attractive links to the different contact forms.
To prevent the bar from being hidden by users you can hide the 'close' button. You can do this by adding some CSS to your site at Design > Custom CSS:
Alternatively, a developer could code an alternative custom announcement bar very easily for you.
Actions would be:
Either make announcement bar permanent or create a dedicated contact bar
Add oncliick scripting so that clicking contact bar links opens the relevant lightbox
Make the content of the announcement / contact bar easily maintainable.
Drop me a line if you want to discuss further.