Have a rough idle that seems to be from a carbon build up any way to solve this

seems like theres a build up of carbon in the intake. you can try the pour in gas tank cleaners for fuel injection cars which you have and after 2 or 3 of those with 2 or 3 full tanks it will clean the injectors and the carbon out of the intake. And if you really want to get them cleaned up even better and stop all the rough idling, take the intake off yourself and clean all the black stuff off anywhere you see it. Thats the carbon build up. Especially on the butterfly valve area. It will not only run better for you but get better gas mileage as well.

yea id definately try cleaning ur throttle body 1st. My 03 1500hd had the exact same bad idle after my battery went bad it would die at lights unless i kept foot on gas i cleaned throttle body runs perfect now took 30min cost 8$ for cleaner at autozone and theres how to videos on you tube

Sounds like a misfire in a cylinder. Check plugs for carbon build up. If carbon on plug, there's a good chance that you will need to replace the fuel injector. Start with checking plugs and then O2 sensor(s). This is steps beyond typical tune-up check. It's especially helpful if you can get a code. AutoZone and KwikLube will run diagnostics for free.

carbon build up in the egr passages and the hose is collapsing

When you changed the egr valve did you clean out the carbon build up inside the intake? if not that could be the problem, if you did, than a peace of the carbon got stuck in the valve, either way your local auto parts store sells a screaned gasget for the egr valve to prevent peaces of carbon from the intake geating into the egr valve, same exact thing happend to me on my 95 blazer.

If there are no vacuum leaks, change idle control sensor.

check throttle body and pcv hoses and ports for blockage possible carbon build up and sticky iac valve

id clean the throttle body before spending more money on anything else, as carbon build up can cause rough idling.
you can clean it with throttle body cleaner, or just gasoline and a toothbrush, then wipe off the build up.

check for leaks around the intake manifold, vacuum hoses and engine breather system. Look for loose wires, check the plug leads. Check the valve lifters for clearances, or faults if hydraulic you should hear them rattling while the engine is idling.Look at the disi cap,rotor and the cap itself for dirt, damp or carbon build up.
I hope this helps

ONE OTHER THING THAT FORDS ARE BAD FOR IS CARBON BUILD UP. THER FUEL CLEANERS THAT YOU CAN ADD TO THE FUEL, I RECOMMEND FINDING A SHOP THAT DOSE A CARBON VAC . THIS CLEANING WORKS VERY WELL BECAUSE IT GETS AT THE CARBON ON THE BACK OFF THE VALVE. WHEN THE VECH WARMS UP THE CARBON ON THEINTAKE VALVE GETS SOFT WHICH IN TRUN ROBS THE FUEL ON THE INTAKE STROKE LEANS THE CYCLINDER OUT , THE YOU HAVE A LEAN MISS FIRE AND ROUGH ILDE