2001 Dodge Dakota Sport runs rough at start up and sometimes engine dies. No DTC's?

I have a 2001 Dodge Dakota Sport with a 3.9L engine and automatic transmission. Engine has been recently replaced with a used engine (same size) out of a 2002 Dakota by certified Techs at a reputable shop. The guy who owned the truck before me never did any maintenance on it and ran the engine with a leaking head gasket until it burnt a hole through the top of a piston and he kept on running it that way until the engine was literally nothing but a big boat anchor. The replacement engine has about 30K miles less than the old engine. When they replaced the engine they put on a new water pump, O2 sensor, spark plugs, plug wires, distributor cap and rotor.

I have no present DTC's. When I start the engine, it runs at about 1000 rpm's briefly then idles down to about 600 to 700. As it idles down it seems to be running on 4 or 5 cylinders and idles really rough. If I try to put it in gear and drive away, it will stumble, cough, sputter, backfire and sometimes die. But if I turn off the engine instead of putting it in gear and then restart it immediately, it will idle down as before but will run much smoother with just a slight bit of rough idle. Then the engine runs fine as I'm driving the truck with the exception of the slight rough idle. The engine seems to have plenty of power and the truck will haul butt when you get on the gas. I just had the transmission rebuilt so I know it's working fine.

I just have that problem when I start it up. And it doesn't matter if it has been sitting overnight or if it's just been sitting for a half hour. Then I have to go through the same routine of starting it twice to get it to run. I could diagnose it myself but I don't have $7,000 to spend on a DRB III scan tool. That's rather cost prohibitive. Any of you Dodge pros got any ideas of what could be happening? I can't afford to keep taking it back to the shop every week. I call this truck "my money pit".

The truck has 118,000 miles on the odometer and the replacement engine has about 82,000 to 84,000 miles on it. I have used Chevron Techron in the last 2 tanks of gas thinking that it may be dirty or clogged fuel injectors. It didn't help. All of the gas in the tank is fresh.