Bumping this - I've had the same issue for about 4/5 years. Original owner, 146k miles on the car now. Replaced plugs, coil packs, battery, carbon cleaning everything, even the HPFP, but not the LPFP.
At this point I don't think it could be anything else since I've replaced everything but the LPFP.
I have a similar issue with my cold starts and I found this video on youtube illustrating the same.
All I have changed is the cam follower and the low pressure sensor (on the hpfp).
I saw your other post about corrosion on the battery terminal and I don't have any issue there.
Have you gotten any wiser about this issue of yours/ours?
Just wanted to leave a final update.
Hard cold start issue is no longer evident. Issue was resolved by treating 3 full tanks with Lucas Oil Products Fuel Treatment.
Overall performance is much improved, akin to getting a tuneup. No issues with starts cold or warm. In fact, car starts like new every time. Also, fuel economy is way up. I will likely run it in every other tank for the time being.
Just wanted to let you guys know. I was skeptical of additives in general, but this stuff really does work.