I have been reading a lot of post here from people with similar problems, but not quite this.
I have a 2007 Ford F150 with the 5.4L Triton engine. A while ago, while towing an 18 ft boat, under deceleration, it started missing i think. Only while towing, and only on deceleration. It kind of sounds like a diesel and almost stalls.
A friend thought it might be the torque converter not letting go. So I had the trans gone thru.
Started towing a camper, and same issue. Under deceleration, under load. I then had the plugs changed. To the tune of $600! No change.
I then recently had the coil packs changed. Thinking they may be shorting out under load. Went and picked up the camper, drove the 25 miles to home. No problem. Great, I thought it was solved. NOT! As soon as I slowed behind my house to park the camper, it did it again. Except this time the check engine light came on. I flashed the code, and it came back P0345 & P0340. (Cam Placement Sensors)
Reading some other posts that suggested resetting the code, I did. Drove to work and back with no problems. No codes.
My question is, what may be causing this to happen only under deceleration and under load. (usually. If it is hot out, it will some times do it under normal deceleration.) I can avoid it happening by placing the shifter in neutral at the start of deceleration, but as we all know, this isn't the safest practice.
Some please have an answer for me!

 

Are the coilpacks and plugs Motorcraft? Also do a few easy and cheap things like remove and clean the throttle body and MAF (with CRC throttle body cleaner and MAF cleaner in a 2 pack from Walmart), replace your fuel filter, and think about changing your 2 upstream O2 sensors (closest to the exhaust manifold on each side). Inspect the seal on your airbox tray that holds your air filter and replace the seal with foam weather stripping for windows/doors. Try the simple cheap things first. I hate to say, but the P0345 & P0340 are potential high dollar codes. I sounds like maybe your truck jumped time due to loose timing chains/broken chain guides or low oil pressure. Be prepared for the worst but hope for the best.

 

The plugs were changed at the Ford dealer. At that time, they said they hooked it up to the computer and detected no misses. The coil packs are not. Cheap ones off of Amazon just to see if it helped. Which it did. For 25 miles until I got in the alley behind my house. No hint of the problem until then. I am also wondering if it has to do with something over heating. All gauges show normal. Oil press., temp.

 

Take a step back and start with those codes. I would start out by changing the cam position sensors on both banks. You also made note that the truck sounds like a diesel before it stalls out. That would lead me to changing out the variable cam timing solenoids. There are many links on the site that explains the pros of doing the upgraded replacement. From what you've described I don't think your truck is jumping out of time on deceleration and then jump back to correct timing on acceleration. If it was that would be a really neat trick. Let us know what you find out. Good luck!

 

So, I came across this video on Youtube, , it described almost to a tee what I was expieriancing. Just had the Variable Cam Solenoids replaced to the tune of $400. They also checked the timing chain tension which was fine. Getting a look at the old solenoids, they did look pretty varnished up. I am going to give it a good work out this weekend to see if it fixed the shutter issue, which I do believe now was the solenoids sticking and keeping the the timing advanced on deceleration. Will post more when I know.