Maybe it would be possible to put all your "setup" code into a single myscript.load() function and then when you've edited your js in chrome devtools, then call myscript.load() in the console to reboot all your DOM events and so on.
Just an idea, completely not tested.
P.S. Just tried your extension using vim to edit a Sass file, while compass watch is running, and your extension is watching my CSS output directory. Awesome to see changes in vim almost immediately appear in my browser!
EDIT: Formatting. Adding P.S.
Have you tried getting in touch with Chrome developers? Printing out info when hot swapping failed would really make you extension useful.
Weirdly, I haven't noticed failures while using the Chrome editor. Might be that I just haven't logged enough hours with it yet, but so far it was working flawlessly.
Speaking from experience, hot swapping JS sounds much better than it actually is in practice. First, as mentioned above it randomly fails with no explanation from Chrome. Also, I find a lot of code I want to hotswap runs on DOM ready and assumes that the page has just been loaded.
On the other hand, CSS hotswapping in Chrome works really well.