HELP: Runing rough after WOT & Differential issues

[RJ's325ITS]

Well guys I have this issue that it's been bugging me, and it looks like it's getting worse by the week.

The Truck:

2001
F-250 extended cab
7.3L Turbo Diesel
6spd Manual
2WD
169,000 Miles

The Issue:

After I do a WOT pull, and I come to a stop (traffic light) the engine is running pretty rough; the whole cab shakes fast for a minute or two, and eventually it settles down going back to normal (running very smooth).

I tried to replicate the issue but it only happens after I go WOT, not even during the pull, during the pull the truck pulls hard too.


What I've done:
Change the fuel filter.
Change the oil.
Do a visual inspection of the charge pipes, everything looks in place.
Change the air filter.
Change the O-rings that leak in the fuel bowl.


Differential Issue:

I have an open diff, or none locking diff in the rear, and every time that it rains and I'm starting to roll the passenger side tire spins.

It's even worse when I'm taking a right turn, the wheel just spins and I have to play with the gas pedal to get traction again.

Is this normal in these trucks?

How hard it is to do a convert ion to a LSD (Limited Slip Differential), or a locking differential?


Extra Info:

Tires are in good condition
I have not change the fluid yet.


I appreciate all the help/tips with these issues guys.

[RJ's325ITS]

Found that the issue of rough idle after a WOT pull was oil contamination thru the crankcase ventilation system, once I build me an intake the issue was gone and now it purrs likea kitten after a WOT pull.

My DIY Intake Rev. A (turbo thru filter)