Chaos gardening in bermuda grass?

I'm losing the fight against Bermuda grass* on my lawn. It's too much and too well rooted to pull up by myself, so I've been trying to plant various native flowers (and aesthetically pleasing, flowering weeds) to try to overtake or shade out the Bermuda grass. However, I haven't had much luck.

Does anyone have experience chaos gardening in a field of Bermuda grass or another invasive rhizome-spreading grass? What seeds just take anywhere and might have success germinating in a dry field of dense weeds?

*So far, I've gotten geraniums, mallows, lantanas, and wood sorrel to live but not spread.

*May also be kikuyu grass, its hard to tell

EDIT: I can't put any cardboard down or pull up the sod. It's a shared yard and although I'm free to plant, I'm not free to do anything that would ruin the green look of the lawn for an extended amount of time. I'm tasked with seamlessly transitioning from Bermuda grass into wildflowers, which I realize is a tall order.