I think this came up before and there were no solutions. But I'm wondering if it's possible to enable walking and using mouse cursors while a dialogue is going on? Obviously the bottom will be black and display the dialogue options, and I'll use SayBackground so it follows the characters as they walk around.
My module (http://www.adventuregamestudio.co.uk/forums/index.php?topic=48218) does exactly this!
You might want to combine it with a background speech module for the exact functionality you described. SayBackground doesn't do talking animations or wait for the text to disappear before continuing with the script.
Edit: I uploaded a little demo to show what it can do when combined with background speech. Check it out! (https://www.dropbox.com/s/zisaqlmgpnak20n/Dialog_Demo.zip)