Id love to say it'll be easy, but AFAIK its going to involve at minimum yanking the engine and swapping to the Gen IV 58x/4x reluctor setup. Once your Gen III is 58x, then you can use an E67 or E38 to run it and control the 6L80E.

The only standalone Ive seen is the MAST setup, but it has an ECM as well. You cant really run these new transmissions without feeding them a proper TQ signal from the ECM, they wont shift correctly and if they do initially, they wont for long (clutch to clutch wears out and without a TQ signal, the TCM cant compensate).

And no, they wont talk to each other. The LS1 PCM is VPW, the T43 is CAN. 2 very different protocols and neither controller has forward/backwards compatibility. The E67 is one of the few controllers that can do both VPW and CAN.