As far as on/off duty conduct goes, in this case with an LTC an employee wouldn't be violating any laws by open carrying in uniform. The only policy broken to my knowledge would be the uniform policy, as the holster and personal weapon wouldn't be part of your uniform. So, I suppose TDCJ could discipline you for being out of uniform off duty. However, an employee could counter with a grievance saying that such discipline violated their lawful right to self defense with their personal weapon while off duty.
I personally do not like to open carry. However, while in uniform it's a bit more difficult to conceal carry a firearm, especially if your carry gun is too large to pocket carry. And, pocket carry poses it's own set of challenges when trying to draw your weapon if the need arose. Changing to civilian clothes to travel to and from work isn't practical, at least not for most employee's.
So, at this point, it appears that to be on the safe side conceal carry is the best option. Either pocket carry, or using a cover garment that meets uniform policy, would be the most appropriate way to carry.