Move primary tabs to the shortcuts bar
The easiest way would be to use the http://drupal.org/project/admin_menu module.

It has an option to move the tabs into the admin menu bar.
Set it by going to the admin menu settings page (admin/config/administration/admin_menu) and checking the "Move local tasks into menu" option.

For users gien access to the admin menu, you should remove access to the drupal toolbar module, or they will have 2 toolbars.

You could even disable to toolbar module and just use admin menu.

If you want to keep using the toolbar module instead of the admin menu module, you can remove the tabs from the page.tpl.php file in your theme and then print them elsewhere.

I don't know off the top of my head how you would go about doing that though.