STOP!!
Please don't go throwing parts at this thing, let's take it one step at a time. First of all what are morning temps where you live? Most places in the USA it's fairly warm, so you can eliminate the GP system, besides you have tested it and know it's working. Drain the fuel bowl, turn the key to on ( not cranking) wait for WTS light to go off, check fuel bowl, is it full? If this is good you have fuel which is good. Next in the morning when you are having problems, I want you to take a multi meter and check battery voltage while sitting and then while cranking. My money would be weak batteries. A PSD requires full power batteries, if they are slightly discharged it will be a real bear to start, this would also explain why it starts fine the rest of the day after first starting it, and when it's plugged in, sometimes a few degrees can make a big difference in batteries. Make sure you check both batteries. Don't just go to the auto parts store because they will probably test good, but as I said we need great batteries not good.
The other idea I would put money on is you have air in your fuel system. Many folks experience hard, really hard starts after changing injectors, the best way to get the air out is run it like you stole it, really hard, this will purge that air out. I would place my bet on weak batteries first. Check what I have mentioned first and get back to me. What are you checking codes with?
NCH