It's good that you can send a eviction notice much earlier in Texas. However the most people wait much more than one month before serving the eviction notice. The judge may favor on tenant's side if you served a notice for the amount owed prior to the service period ending.
For example, Tenant owes you $900 by 1st of November. You served the tenant for the same amount on 20th of November. They may argue that they only occupy the property 2/3 of time. The actual owing amount should be $600 with prorated amount.
The second point is that you want to show the court that the tenants owe significant amount to win your case. If you rush with a notice with less than one month rent, it might be a little harder to convince the court to grant defaut judgment and writ of execution.
