What you need ... is a bit of jQuery that does the following:
create a frame on the right, to hover over the starred posts with fixed formatting (thus occluding the star list, since it's there, and you can ignore it) such that the frame contains the following: a label, a textbox, and a textbox.
label: "Enter message ID here"
first textbox gets messageID
onblur takes messageID and finds the dom element (using jQuery selector) and makes second textbox the HTML of the whole message element but HTML encoded so you can copy and paste into a spot on MSO
then it's messageID, copy, alt-tab, paste
you could even put in code that when you click on the textbox it will auto copy the contents to the clipboard for you
all-in-all, that sounds like too much work, so I'm not gonna do it :p