Without an export/import settings option in the plugin; the only way I was able to accomplish this was to copy the data from the database of an existing installation with the desired options and toolbars layout.
How to do it:
Open the wp_options table of the database on the WordPress installation that already has TinyMCE Advanced setup the way you'd like it, and search for the option_name 'tadv_options' and 'tadv_toolbars'. Highlight and copy the option_value for each of these and paste them into the same database table of the new installation.
I keep these option values in a text file on my computer for easy copying and pasting to each new installation.