You should be able to reload the iframe via:
To grab the favorites iframe you should be able to do something like:
As mentioned by Daryl, the above will just reload the entire UI in the iframe. The following code uses the API to unload the lists in the favorites which should cause them to reload... I've only tested real quick in the console though.
Hope that helps!
For me my final solution was very close to Alex's reccomendation. I just had to get a different list, I used