Power-line easments?
Only if staying put or any other route was life threatening.
I agree with others here, who say "stay on real roads".

However, can you go directly East or directly West for 100 miles
and then turn North?
I just realized that Fort Worth is west of Dallas so forget that!

What sort of event were you thinking about?
Chemical release?

Hurricane/flood?
For weather related, staying alert and being decisive
can give you a head start over others, so main roads
could be empty. Having wife and kids go to a safe
area/vacation-spot ahead of time, could cut down
on your prep time.
Perhaps you can make a decision and start in 5 minutes,
but your wife and kids would take at least an hour, Im thinkin.
If kids are in school, maybe it would take more than an hour.

If you evacuate early a few times, you can expect to be criticized;
so keep your own counsel, if you can.