In Kalifornia, I believe that the legislature has been in the habit of "stopping the clock" through a vote of its members in order to satisfy the requirements for passing a budget while actually passing it at a later time.
Perhaps the Texas Senate, convening in New Mexico, just needs to pass a resolution " that for the purposes of this session, Albuquerque, New Mexico shall be considered part of Austin, Texas".
This might even get the attention of New Mexicans who might fear an armed invasion and takeover of their state. This might be a good thing. The New Mexican State Police might escort the whole bunch back to the border with a invitation to solve their problems elsewhere.