This is an interesting question, with some interesting side questions coming up as parts of the answers. So, I will attempt to deal with the original question, as I see it, and then may mention some other points.
To recap, the original question was if the poster could enter a private parking lot with his gun in his glovebox, if it is properly posted for 30.06. The logic was that he was not carrying under the authority of the CHL at the time.
First, we have to ask if anyone without a CHL could do this. They are not carrying under the CHL but under the current unlawfully carrying law. Is it illegal for you to enter the parking lot with a gun if you are not a CHL? Obviously, the original poster felt he could do so since he was locking the weapon in the trunk to avoid carrying it under the CHL authority.
Here we have an interesting quirk of the law that will probably get someone's attention in the next legislative session. A proper posting for 30.06 only applies to CHL holders. It is not notice to anyone else that a gun is not desired on the property. Unless they also post the traditional no guns signs, the non-CHL can carry in his car there. Remember that this was done because, at the time, the CHL was the only way to carry on a regular basis so no one though they would need a non-30.06 sign for the others. It was not true even then, but the odds of a person who was traveling entering were pretty small. So, what we have under the current law is a wierd case where a CHL could be banned but a non-CHL has not received their notice yet.
But if we look carefully at the wording of 30.06, it only applies when you are carrying under the authority of your CHL. If you are carrying under some other authority, you can ignore it. In this case, you are in a car, so you are not carrying under CHL, but just exercising a right where there is no law forbidding a behavior. Thus, you cannot be charged under 30.06.
So, my answer to the original poster would be that the 30.06 sign does not apply to him in the car. It is, for the current time, and only until someone realizes this, virtually impossible to stop a person in a car from entering a parking lot without posting multiple types of no guns signs, one of which must be 30.06.
An interesting second question was if there was a precedence to which authority to carry was being used if multiple authorities exist. The answer is yes and no. There is no legal precedence beyond the wording of the law itself. Remember that being in a car is now an element of the offense and not a separate authority. Your CHL does not come into play until you exit the car.
Can you have multiple authorities? Of course it is possible. This Saturday, I will be driving to Dallas for a convention. I will be covered by the law not applying in my car, the traveling exception, and my peace officer status. If I had a CHL, I would have another exception still. Does it matter which one is higher? No, since they all apply to say the same thing. They only time the fact that I have multiple exceptions would come into play is if I went somewhere that the traveling did not cover but my peace officer status did.
And that brings me to the other interesting point. When a peace officer is carrying and has a CHL, does he have to show the CHL to the other officer that stopped him? Yes, he does by law. The important point to remember is that the law on displaying the CHL does not say carrying under its authority. It simply says you will show it if you are armed. So, the peace officer who does not show his CHL is committing an offense. In the real world, it would probably never get noticed or reported, but it is an offense anyway. This is the same as if you are carrying on your own property and have a CHL. You are still required to show your CHL when asked for ID. You are not carrying under your CHL authority but you still have to show it.
The other rules on carrying (PC 46.035) specifically state carrying under the authority of the CHL. So if an officer has a CHL and carries in one of those, he is not breaking the law. But if he fails to show his CHL when he is asked for ID, he is breaking the law.
As an aside, most officers who I know of who get CHL's do it just to get around the NICS test. I suppose some are issued to undercover detectives so they can claim they are not cops when the people with them find them carrying, which is the reason for the "alias" CHL. An alias CHL is liek and alias DL. It helps the undercover officer build his role and keeps things off his record as he is investigating. It is mostly done so if a bad guy does try to run him, he gets a real return on the fake name.