You have to dig it out, unfortunately, which is no small task. I got so fed up with mine, I gave it away years ago. It was ugly and never bloomed. The blooms aren't very pretty either.

Would it help to kill it first? A little Round-up or little bit of chlorox poured directly onto the stump? Once it rots it should be easier to get out, right?

Yes, get it out of there while you still can!
They get huge and grow into a huge clump.

white bird of paradise before I spent months of cutting and the hired guy gave up on digging it out
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finally had to hire another neighbor with a backhoe
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save yourself before it's too late.....:-)

I made the same mistake, planting BOP too close to screened porch. However, I dug up and moved the entire plant to a better location without trimming it to the ground as you have done.

The root ball was huge and filled with a nest of baby ringneck snakes. My BOP probably weighed 150 pounds and was incredibly difficult to move. It took the abuse well and is very happily growing in a good location now.

Take care of yours before it grows back. It will grow back. With a vengeance. Best wishes!