Well....that looks like quite a nightmare!
First some background on these cars/engines. The engine management system on these vehicles is called Computer Command Control (CCC). All that the computer system does is to adjust the engine to make it run efficiently. It will run without the ECM hooked up/plugged in. Secondly, if it is backfiring and sputtering then there is a fuel/ignition problem. White smoke can mean a piston ring issue, or in some cases I've seen plugged catalytic converters cause backfires and white smoke (if it still has a cat). Last, a lot of the wiring under the dash is for the engine controls system that is just an input, not an output.
As far as repairing all of this, my advise would be to unplug all of the CCC connectors and tape them up out of the way. You do not need to cut them off. Also unplug the 2 ECM connectors (the ECM is under the passenger kick panel). These wires all come from the passenger side harness. None of the wires on the drivers' side are part of the computer system. You may also need to remove the Check Engine light bulb in the cluster.Next, remove the carb and distributor and replace with non-emissions equipment. An older 4-pin HEI distributor and any pre-1974 Quadrajet or other spread-bore 4-barrel without any emissions equipment would be your best bet. Remove all of the unnecessary vacuum hoses, then go through and tune the engine as you would any traditional V8. If it still has a cat, remove it and see if the smoke clears up. If it doesn't, then it is either a fuel or piston ring issue. As for the wiring under the dash, that looks like one hell of a mess and you may need to find a factory wiring schematic to figure all of that out.