I have not upgraded my Gemfinders yet, so I can't try an iteration of it. That said, I like the looks of it, but it seems like it is going to be too much to ask for those four Amethyst Towers to do so much work.
You can't play the cats until you get a tower. You have to get a tower before you can Supernova before you can Patience.
Will the Wardens be enough to keep you alive that long?