Hesitation, misfire or "bucking" feeling

If your plugs are good on those quad engine i change lots of ignition coil and the cover plastic crack and the spark jump check the video

PO 316 -- is a misfire on the first 1000 revolutions

You get that & sometime a lot of other codes you ignore

You may or may not have PO301 thru PO308 codes
The last # is the cylinder

1,2,3,4 Pass Side
5,6,7,8, Driver Side

Front to back

All you can do is buy one new coil and try it in
a cyl with a code or you may have to walk the
new coil from one cyl to the next and drive few
days in between.

The other choice is a repair shop with an oscilloscope
and the inductive coil pick up adapter

Buy one new coil from auto parts store $59.00

Walk it one cylinder at a time

Why would you swap coils,obviously one
of them is bad.

The one you took out of #5,find it ,and put in the
new one there.

I would put in new OEM Plugs.
They are a special tip just for the LS
at least on ones newer than yours
They are NGK even though they have motorcraft
on the ceramic shell.

Clean the throttle plate and MAF with the two
CRC products for that

I wouldn't rule out a bad EGR Valve as another issue,
though not related to the misfire issue

EGR Valve-is where I would start.
Remove and plug the vacuum hoses to it,
road test,problem solved,replaced EGR

After that, expect to loose 1 or 2 COP Ignition Coils a year
Any MIL Lamp on dash,you retrieve the code and go from there
Any PO301 thru PO308 if you have a V8 is a coil misfire
very,very common on the LS and most fords back to 1998
with coil-on-plug

Next clean the throttle plate and MAF Sensor
CRC Throttle Body Cleaner & CRC MAF Sensor Cleaner

Next TPS-throttle position sensor gets tested

I hope you have changed the spark plugs every
three years,regardless of milage,they are a special
NGK Plug just for the LS

Also you have to use premium fuel,sorry in an LS

When you get a coil misfire, the PCM starts to cut
injector timing and you get just what you discribed

V8-1,2,3,4, Pass side Front to back
5,6,7,8, Driver side Front to back

PO 303

V8
1,2,3,4, Pass Side,front to back
5,6,7,8, Driver Side,front to back

1,5,4,2,6,3,7,8

Clean MAF--CRC MAF Cleaner
Clean Throttle plate--CRC Throttle Body Cleaner

drain your transmission,and while you have the pan off,replace the transmission filter. refill to level specs. also replace the air filter and pcv valve.

Fuel filter

check your transmission fluid it might need serviceing

I was having the same problem between 40 and 50 as well as the miss fires after changing a coil that was miss firing one it reached running temp. the problem vanished so check your coils.