Bermuda grass experiment

I live in Missouri, and my yard and garden beds are absolutely taken over by bermuda grass. I have tried hand pulling small sections in the garden with mixed results – it takes hours and by the end there is always guaranteed to be a root or two missed.
I like to avoid chemicals if at all possible, and I want to do an experiment this year to see if I can out-compete the bermuda grass in a section of my yard. I’m willing to try anything – it does not need to be low growing “lawn” plants, (I eventually want to change a lot of my lawn into native permaculture anyways!) but they must be easier than bermuda grass to eventually remove after the bermuda has been successfully smothered.

So – what are your best ideas for aggressive plants? I know bermuda has really deep roots and dislikes shade. So if the plants provide a lot of shade/take up a lot of root real-estate you get bonus points! A couple ideas I have already is sweet potatoes or native buffalo grass.

Thanks everybody. 🙂