In the end, zoysia will take over unless Prograss and Sencor are part of the weed control program. You do not want zoysia unless you can mow with a correctly adjusted and sharp reel mower. When I have looked at weedy bermuda lawns, factors contributing to the weeds were fertilization and mowing. Bermuda mowed at the right height, with the right machinery does not allow weeds. Bermuda fertilized near 1 lb of N per month of growing season and mowed at the right height grows dense enough to overpower many weeds. Bermuda mowed at over 1/12 and with a rotary is usually thin. Thin enough such that every possible weed comes up. Low mowing tends to discourage grassy weeds that tend to grow tall and clumpy. If it is not feasible to mow low, then that area is best established with centipede, St Augustine or cool season grasses. Listen to ArTurf. Preemergent can and does thin out bermuda. You do not want to do anything that thins out the bermuda. In bermuda, there are lots of postemergent chemicals that are selective to the bermuda. I have to use the term postemergent loosely because many of those chemicals were originally marketed to corn and wheat farmers for season long control of most weeds, both broadleaf and grassy.