...shoulder chest holster...
What differentiates a "shoulder chest holster" from a "shoulder holster"? Is a "shoulder chest" the same thing as a "shoulder"?
if there is a difference, what makes you believe carrying a gun openly in a "shoulder chest holster" as opposed to the mandated "shoulder holster" or "belt holster" is legal?
Here's what I suggest. If you want to carry openly in TX with a TX handgun license to carry, get yourself a shoulder holster or a belt holster
as mandated in TX law. Don't get a "shoulder chest holster" because that's not what's mandated in the law for open carry. Don't get a "belt arm holster", or a "shoulder stomach holster", or a "neck shoulder holster" or an "calf ankle holster" or any other type of holster that's not a shoulder holster or a belt holster. Don't get a chest rig and call it a "shoulder chest holster" in an attempt to make it sound legal. Don't get a pocket holster and call it a "belt pocket holster" to make it sound legal. Any holster maker or seller will be able to help you pick a holster that is a shoulder holster or belt holster and will help you differentiate those two types of holsters from other types of holsters. That is useful since
all other types of holsters are not legal for TX open carry.
Get a good one, one that you can wear comfortably while performing normal everyday operations like walking, driving, bending, sitting, etc. so you don't have to take it off and put it back on all the time.
Since you won't have to take it off and put it back on, you won't have to worry if having it IN a shoulder or belt holster but not actually WEARING the holster is legally problematic. You won't have to worry about the period of time while the gun isn't being worn but is being exposed.
This will take care of the concerns you have mentioned so far with regard to TX open carry law.
If you do not want to carry in a belt or shoulder holster all is not lost. TX law allows a permit holder to carry via ANY desired method if the handgun is concealed.
So there are your choices. Wear it in a belt holster or shoulder holster openly. Carry it any way you like as long as it's concealed. Pick one. Done. Easy.