I have tried for 3 years to get this growing between my pavers and in some places it's kind of ok but mostly it just keeps dying out. Doesn't seem to be related to water. I've finally called it quits and I'm having it grouted with cement. Enough is enough.

It's only toxic if you ingest it, I've planted if for years and I have dogs. Never an issue. It does not sound like you are planting it with your edibles, just near them. You can maintain boundaries by trimming with a serrated bread knife. Best garden tool ever. It's never been invasive for me, I have it as a carpet under annuals and fuchsias. I cut each cell of a six pack in half to get 12 pads to plant instead of 6. It spreads moderately. Check creeping Veronica (Speedwell) if you want a similar performer without the toxicity. Lots of plants we use are poison, daffodils, tulips, and ivy, oh my.

Blue Star spreads by rhizomes and one of the easiest to propagate and obvioulsy it likes the mositure, not too wet that it gets now, possibly because of the lawn watering so you may nto be able to cut back on the watering. For repacement of the lawn area that it has overtaken I can see no option of ridding of the grass without disturbing the creeper so you might want to dig up the plants and pot to baby and then sufficate the lawn either with cardboard or other means and then replant the creeper. The following link shows how to propagate plants that spread by rhizomes. Here is a link that might be useful: Propagating Perennials

It spreads very well. She was recently mentioning that it's spread into her beds so much that it's saved her a bunch of money- instead of buying more flats she can make plugs from what has overgrown her pathway to finish off the space she has to fill. Your area looks well contained, hers does not have any edging to keep it in. Her system is set up to water for 15 minutes twice a week right now and will change back to three times a week when it warms up.