Buffalo grass eradication / tall fescue establishment
Buffalo grass - the only real native turfgrass to North America and one that has a stoloniferous warm season growth habit that is low growing with a grayish/green color has its uses and is also a functional grass for roadsides, soil stabilization, ect. It is also like any of the other warm season turf grasses hard to entirely eradicate. This process will take time and there is no instantaneous method.
Glyphosate ( round up ) use is a good low invasive methodology and the best alternative to excavating and ripping up ground, it also keeps costs down. Now that the buffalo is in dormancy the timing is off and wrong.
Glyphosate blocks enzymatic action, in particular EPSP synthase which aides in active transport of protein synthesis in all higher plants, it is taken in through actively growing foliage and translocated down through food conducting tissue known as the phelom. It then gets taken to perennial parts and storage organs where it completely destroys the plant.
Usually a minimum of 2 applications spaced 3 weeks apart at the max rate work well up to 90 - 95 % control. This needs to be done during the growing season, even with this strategy there can still exist some live stolons that will repropagate and will take avid follow up after the fescue stand is established.
Next year is your target for this work. I suggest slit seeding the fescue in 2 ways to ensure maximum uniformity of the stand as this is a bunch type grass and propagates laterally only a few inches from the plant, the fescue will also require annual overseeding to keep the stand thick and choke out any buffalo that tries to encroach back.