To others: Dillon is trying to attach a function to run after just one specific widget is done loading. While trying to run a function after the whole page is loaded is challenging, just doing it after 1 widget isn't as tough.
Dillon, since it's your own widget that you're trying to tie into, can you not add an empty function called "onWidgetRendered" that gets called wherever your widget is actually done the dom rendering?
Once you had that, you could use aspect.after to attach your custom function.
You are not the first one looking for this, and there is no easy answer:
Suggestions:
The only things that worked for me where:
For this specific thing I created some Javascript widget a lot like the HTML snippet in which I recursively call a function until some object is found on the page. After it is found it quits the loop and triggers the callback function.
To be sure the loop is not endless when the object is never found, I added a parameter to call it a fixed amount of times and if within this time it is not found (lets say 10 seconds) also end the loop and don't trigger the callback function.
So, actually, option 1 that Chris is mentioning would be a go for your problem.