I recently bought a house here in Sacramento, CA. I have a 40x40' backyard that the previous owner neglected. For the most part it's in okay shape, but as the topic suggests, I have a big problem with dallis grass! It covers probably 1/4 to 1/3 of the whole lawn. Most of it grows in one area, but there are a few patches in other spots plus individual bunches dotted around.. I'm reaching a point of desperation!

I've looked around online for various advice on removing it, but it doesn't seem like someone in my situation has hope?
So far, I have tried:
1. Mowing the dallis grass very short repeatedly, but it just came back
2. Spraying the entire lawn with "Safe for lawn weed killer", which I have done three times with no effect on the stuff at all.
So, I finally resorted to using RoundUp on a few bunches to see how it would work, and sure enough it killed them (at least the blades, the roots/rhizomes are another matter). However, I'm left with a big dead mound, which I don't think my regular grass will overgrow. So I pulled a couple up, but was a huge effort and there were still huge rhizomes down deep which I don't know if they'll just come back. And the result is a crater.
While this could work for the individual bunches dotted around, I don't see this working for the patches or the largest area (we're talking 100+ sq feet). So, while nuking everything with RoundUp might surely kill all of it off, it's not as if my grass will naturally grow in, because the dead dallis grass still leaves a big, tightly-bunched mounds.
Do I have any options here? Do I have to throw my hands up and hire a lawn care service to just nuke my whole back yard? Any help or advice would be MUCH appreciated! Thank you!!