I'm having the same issue when my car sits out in the cold all day at work. It shakes under partial throttle until it heats up. Seems to be worse if the heat/AC is on, probably due to the increased engine loading. Today I got my first misfire on cylinder 1 with the following codes.
P29CD - misfire cylinder 1
HSAAF - fuel pump plausability
H2FDB - Short circuit or signal interruption
H2FCA - Short circuit or signal interruption
H2FDA - Short circuit or signal interruption
Most of these codes I cant find much info about. Especially the short circuit ones.
I am going to check all my ECU wires and coil connections. I plan on swapping coil 1 and 2 to see if it follows that. My plugs were replaced less than 5k miles ago. Seems like it could be a leaky injector. If so, I may try to code that myself with a D-CAN cable and INPA.
I hope its not the HPFP because that was replaced last year and my warranty is out.