Tenacity does wonders on crabgrass, but there are lots of alternatives that are cheaper. For TTTF and Rye, you can use it both spring and fall and not go over the yearly app rate, even if you do two apps each season two weeks apart (I always do for spot weed treatment). I've used it to help knock down Poa Annua and take on some other stubborn issues while also buying me time if I overseed at the same time.
Sounds like you have a larger yard so I don't know how far it will go for you, but I'm sitting on around 8k sq/ft of yard and a bottle of it has lasted me years with as little as I use. I don't blanket spray it unless it's as a pre emergent and will only put down one blanket app and spot spray any issues in areas not newly seeded two weeks later.
Does take awhile for the white areas on weeds and where good grass goes lighter green with mild damage to come back so I don't use it every season/year.
If you didn't have any issues with that Black Beauty Ultra and didn't have anything down, I either had a batch with issues or the seed came from something else.
I'm also around 8k sq.ft. I've never used tenacity, but as mentioned, I plan to get some and apply it before reseeding again next fall. I'll do some more research to see whether I should use it for pre in the spring, versus other options, depending on budget.
Poa annua is a small issue for me next to the street and may use tenacity or another pre there next fall instead of trying to reseed those areas. Both PA and crabgrass need years of pre-emergent apps to prevent all of the dormant seeds from sprouting, but that can also interfere with reseeding projects.
I'm planning on reseeding at least another fall or two before trying to tackle the poa annua so I've got a decent stand of grass from the neglected yard previously.
It's also going to take some time getting the soil healthy with compacted clay, but I hope to eventually get to an all organic program.