Ford 7.3L Power Stroke (1999-2003) :: Hard To Start When Cold Outside But Eventually Fires Right Up

My 1999 F550 7.3L has been hard to start when it's cold outside since I got it with about 150k on it (it has 200k on it now). Last year we tested the glow plugs and sure enough 5 of 8 were bad. So they are all new now. It worked a little with the hard start, but not much.

When it's cold out the engine will crank forever amongst clouds of smoke and the smell of unburnt diesel fuel and sometimes eventually start, followed by smoke and sputtering until the cylinders clear out. However, what I have noticed recently is that it will sometimes start in the first few revolutions. It seems like the best way to start cold is as follows:

1. Let the glow plugs heat up for a minute or two,
2. Crank engine for 10 or 15 seconds and stop,
3. Crank engine again, but stop if it doesn't catch in the first couple of revolutions,
4. Repeat step 3 until engine starts.

When it starts using this method, it's immediate and it's running smoothly immediately with minimal smoke. This is making me think there's a computer or sensor issue, but I have no codes.