I've seen the question and have thought about how, or whether, I can be helpful. Unfortunately, the question of whether a
Wyoming LLC needs to register as a foreign entity in any other jurisdiction under the circumstances you describe is simply too tough to answer appropriately in a forum. It is one of those questions I tackle for clients and rarely can give a black and white answer.
I would say that generally, once you have employees in the state (or owners performing services in the same manner as an employee), you are doing business in the state. From the facts that you gave, that would likely mean that the LLC is doing business in Texas and would need to register as a foreign LLC in Texas.
Your activities in New Jersey sound more incidental and more like an owner providing broad oversight, so it seems at least more likely that you could take the position that the LLC is not doing business in New Jersey.
Those are just general thoughts, however. I am not familiar with the details of the laws in New Jersey or Texas with respect to foreign LLCs, nor do I know the consequences in those states of a failure to register if it is in fact required.
In other words, you should talk to an attorney who is either familiar with the laws or who can spend the time to review the requirements of the two states.