You could move to Dallas for a while and apply for the document changes there. I hear that many of the judges in Dallas will issue the Court Orders. And if you do run up against a bad one, then you can keep reapplying until you get one that will grant it.
I recall from law school that, under Federal Law, one becomes a resident of another region in the US when one "enters the new territory with the intent to reside permanently therein." I did a little research on Texas Law, and Texas requires that you live in Texas for 90 days and have a Texas dirver's license, before being recognized as a resident of Texas. I could not find anything specific about residency requirements for individual counties, so it may just be a matter of getting an address and changing the driver's license.
I think if you temporarily moved in with someone in Dallas while you prepared to find work and your own place and later move your stuff to Dallas, and changed your driver's license address to their address, then you could go ahead and apply for the Court Orders in Dallas. In the meantime, if you spent a lot of your time at your present place, and only traveled to Dallas once in a while to look for work and look at apartments, that shouldn't have any bearing on your status as a Dallas resident. And if you later changed your mind about moving your stuff, and changed your address back on your driver's license, that shouldn't invalidate any Court Orders you already obtained in Dallas.
But luckily, you can still go to Phyllis and get them done, so I guess you can save that as a backup plan.