Engine will not start?

My car listed above Limited with the 3800 engine has had an on going but periodic engine misfire problem. Above an outside temperature of 60 it runs great, between 60 and 50 it starts rough (really rough) then runs fine (without a misfire) after the engine warms up. Below 50 it won't start at all. Between myself, my buddy the mechanic and a couple other shops in town we've replaced the following: plugs, wires, ignition coils, ignition module (I think, but the replaced ignition module is too hot to touch after just a few minutes running), fuel pump, fuel filter, fuel lines to the firewall, fuel pressure regulator, crank position sensor, intake air temperature sensor and we've cleaned the EGR valve with Seafoam, got the valve moving pretty well, but we might be able to do a more thorough job. It did seem to start at a bit lower temperature after cleaning the EGR valve.
I borrowed my buddy's Matco diagnostic computer, and got some data the day after, old codes for EGR, crank and cam position sensors, and knock. I watched the data feed, but don't really know what to look for. The EGR position was better than 90% correct but it was running well then. It's been too cold to get the car started lately maybe this weekend! So where do I look next? Clean the EGR again, or replace it? If a brand new ignition module is suspect, what might be causing it to run hot (if that's not normal)? Both are $150.00 parts. Cam shaft position sensor? I'd appreciate knowing your rational. How is your diagnosed problem affected by temperature? Thanks!