The only thing that will kill bahia is Cimmeron. It used to be sold under the name Ally. It can now be bought under the name Cimmeron and Cimmeron Max.
Yes, it is expensive. Mentally divide your pastures up into managable portions and treat one portion at a time. For example, we knew we could afford to manage 35% of the pastures at a time with Cimmeron, so we are only treating 1/3. Next year, we will do the next 1/3.
Good luck.
PS - Call Producers Co-op and ask for Carl in the fertilizer plant. Ask Carl to come out and look at your pastures to give you recommendations on effective and efficient ways to improve the conditions. He saved me thousands of dollars in potential pasture rehab. If you are a member of the Co-op, this is a free service. (And Jon G doesn't know range grasses.)