Hi Haley! That is certainly the age-old dilemma. Something that I've learned from property management, is that a lot of times, the higher priced rental homes take much longer than the $1k-2k range. Like significantly more. And that can definitely eat into your year-long returns on a rental property. So don't sweat so much not being able to get an expensive home right now. That's not always the case, as we got an expensive home in Keller rented within 2 weeks of listing.
Since you are downtown I'll make a couple suggestions:
Have you looked into duplexes around White Rock Lake? I think anything on the West side of the lake you are good on for your commute. The east side you'd probably want to stick to the lower half of the lake. I have a client who is doing exactly what you are looking to do: live in half a duplex and house hack the other half - granted she's using property management services so she really doesn't have to interact or deal with the next door neighbor in case something goes south. She lives in the M streets at a not too expensive duplex.
Another option is to find and refurb a distressed home. My company owner does this all the time for clients and we have really good success and the client-owner's have all been very pleased and gotten good rent returns. When I was looking for my first home, I found a bunch of distressed properties off Mockingbird towards the lake.
A third option would be to go to the Bishop Arts District or one of the up and coming areas in South Dallas that is becoming gentrified.
Hope that helped!