Although I agree with your conclusion that the controversy needs to be put to rest, I disagree with the use of "Lah Tech" and support "L-A Tech". Now that I've made my position made, hear me out:
There are four Techs that matter: Louisiana (first of course), Virginia, Georgia, and Texas. All schools are often abbreviated by their two letter state designation: LA, VA, GA, and TX.
Louisiana Tech is the only state that pronounces their abbreviation. I live in Virginia and nobody says "Vah Tech" or "V-A Tech", they say Virginia Tech. Similarly, nobody says "Gah Tech" or "G-A Tech" or "Tix Tech" or "T-X Tech."
Ours has caught on (both "Lah" and "L-A"), but similar to ULL trying to convince the masses to drop the "Lafayette" it isn't going to happen. I agree with your Ole Miss and Mizzou conclusion that the abbreviations are good for marketing.
People who confuse "L-A Tech" with "Los Angeles Tech" are both an extreme minority if any exist and simply look uneducated if they say were to say that out loud. Example - I was in the Navy with an LSU graduate. We were out in DC on a Saturday, and he was wearing an LSU shirt. Someone from Brooklyn asked if he attended Long Island State University. Everyone laughed at her because of what she said and then we laughed at him for looking so disgusted. Is LSU going change anything because of a person like this? No.
Similarly, we are not located in France - "Lah Tech", which could be translated to "The Tech" from someone outside the U.S. .... Are you trying to endorse the commercial?!?
For some reason I associate "La" with "Lah" and "LA" with "L-A". Since our logo often shows up as LA Tech when abbreviated, I simply associate with "L-A Tech."