As the most simple solution, you can connect 8 I/O pins of your µP, presuming it has fully controllable pins, not like the "poor-mans" output pins of a 8051. I don't understand why you are considering about "inverting" feature of the tri-state drivers? As far as you reported, you want to be able to set the output to L, H, and Z, which is actually possible with both driver flavours.
HC125 gates are a suitable suggestion, analog switches or multiplexers would be anothe way, also allowing to drive different voltage levels to the device under test.
You didn't mention any condidtions like speed, logic level, required ouput current, acceptable leakage. Using I/O extenders is just an additional question of your exact setup, and beyond the scope of the original question, I think. Of course you can use them, if they offer an advantage.