As you state, the print functionality is ActiveX, so it will not work in Firefox.
You could place a button in the "msrs-buttonHeaderBackground" div using a javascript button.
I found the div using the firebug firefox extension - it's great.
You could possibly find the other divs you'd like to hide and put them in a print style sheet, so they don't show up when going to print.
http://www.456bereastreet.com/archive/200709/how_to_create_an_unobtrusive_print_this_page_link_with_javascript/
I agree with the author that ctrl-p could simply be pressed for a similar result instead of adding a button - but the print style would still help in that.
You know what...I just realized something. You will not be able to print a page that is more than one page! Ouch.