I was in your shoes a few years ago and looked all over Dallas County. PlaneSmart at ADS is super expensive though they do have a few 172s, but otherwise I think the only shop that will do rentals at ADS is the Addison Flight Club which, in my opinion, is not going to be a reliable way to rent a plane with such a small fleet.

I built a ton of time at Monarch, but unfortunately they exited ADS a few years ago. If you're willing to drive up to North Texas Regional (GYI) I highly recommend them. But that's a long drive, but maybe it's doable once per week? There's a school named Airplanes & Attitude at TKI which had a great and helpful team and I think they rent. Otherwise look up the smaller schools at TKI and RBD as they may also rent to non-students.

For Tarrant County I'll defer to the others, I think Arlington (GKY) has a number of shops that will rent.

And finally, after typing all that out, have you thought about starting your instrument training and using that as a way to build experience and confidence? Looking back I feel like I made the biggest skills jump in my overall piloting during my instrument training. So consider that as well!