You do you. I think you are doing it wrong.
Except that, whatever the law might be in your state, my state explicitly allows all vehicles to turn into any lane when making a left turn. So while whether you are doing it right or not in your state may be an open question, in my case, it is definitively not.
ETA: And just so we’re clear, this is a problem I have never had, because I have never made a left turn in the way you seem to think your state requires you to do it:
So, very real problem, and one entirely created by this (IMHO flawed) idea that a cyclist should turn left into the left lane rather than the right.
It’s a legal requirement here.
If I ever ride in TX, I’ll keep your laws in mind. I doubt this will ever come up since I can never see myself riding on multi-lane roads there.