re: Is this a loophole option?

Correct. You can say you purchased it for however much you want as long as you are both LA residents. If they look into it then they have the authority to tax you based on FMV; however, they very rarely will go that far.

Anyone transfering a vechile from out-of-state will have to pay taxes, and will get a 4% credit(which is the amount due to the state), but still owe city and parish taxes.