Killing the bermuda before you dig it out just helps to keep it from sprouting back from the bits of root that get left behind if you try to dig it out.
You'll still need to dig it out to get rid of the dead roots, if you want to be able to cultivate as usual once your intended plants are ready to go in - or when the bermuda starts coming back.
(A cement mixer with a generous amount of water is a good way to separate the roots from the soil, once the roots are dead, according to a neighbor who used the method?)
The exercise potential is still there - but it's more productive exercise without live bermuda roots in it.