The true cause of your catastrophic EGR cooler failure is the oil cooler. That needs to be changed as well, and that requires the removal of the intake manifold. While you have the manifold out, cleaning it would be a given.
You should also split your turbo and cleaning the exhaust drive side of it. The leaking egr cooler leaked coolant into the up-pipe on the passenger side and the coolant was forced through the turbo on its way out of the tailpipe. Mix soot, heat and coolant in the turbo and it will create a gunk that will interfere with the free movement of the unison ring that moves the variable vanes.
This whole repair (oil cooler/egr repair and turbo cleaning) is covered in detail in a thread that is linked in my signature line (click the "step-by-step" link).
How your engine hydrolocked is that the cooling system pressure forced the coolant to leak out of the failed EGR cooler. The coolant then ran down the up-pipe on the passenger side of the truck and into the exhaust manifold. The coolant then entered through whatever cylinder happened to have the exhaust valves open.
To clear the hydrolock, you will have to purchase a new glow plug harness for the passenger side of the truck, remove the existing harness and pull the glow plugs on that side of the engine. I say to buy the harness ahead of time because there is little chance you will be able to get it off without breaking it.
Now for the REAL cause of this whole nightmare:
Coolant. The Ford Gold coolant requires frequent and careful monitoring of its additive package (The FORD TSB can be found here
Once the additives are depleted the coolant can create a gunk that plugs the coolant passages in the oil cooler. The coolant that leaves the oil cooler is fed to the EGR cooler. The plugging of the passages in the oil cooler will slow the coolant flow. The egr cooler has to deal with VERY high heat and a compromised coolant flow will cause the egr cooler to overheat. This overheating causes it to fail.
What to do now? Well, your in a pickle. There really is no safe way to flush this junk out of your engine with a failed egr cooler to the extent that you have. You will have to flush your cooling system after completing your repairs. This flush has a very real possibility of causing a very short lifespan of your new oil cooler. All the junk that you must get out of the cooling system can deposit itself into your new oil cooler. The coolant (and oil) enter and exit the cooler from the top. Anything in the coolant can settle to the bottom channels and is impossible to remove.
The one and only way around this is to do your egr cooler delete, clear the hydrolocked condition, then flush the engine. Once the flushing is completed, you then replace your oil cooler.
It is HIGHLY recommended that you change coolant type. You could stick with the Ford Gold and do all of the continual testing/adding if you wish, but if you change coolant type to a CAT EC-1 rated ELC coolant, you will not have to monitor the additives. Not to say this coolant is a "fill and forget" coolant, no coolant is. You should still change this coolant every two or three years, but it does not create the junk in the cooling system that the Ford Gold is well known to do. This is also no guarantee against future failures, but the track record of the ELC style coolant is much better.
Now, the flush: Check out the "nylyon" link in my signature line.
There are two chemicals that need to be used. One chemical is to remove rust scale build up. The other chemical is to remove the film that the Ford Gold coolant deposits on the walls of the cooling system (for cavitation control and corrosion resistance). If this film is not removed, a chemical rection could occur between the ELC style coolant and this film which could land you right back where you are now.
What else do you need to do?
You desperately need to install an electronic monitor (especially towing long distances with this engine). You need to know what is going on under the hood. If you had one, and knew what to watch for, you would have seen all of the above long before the egr cooler failed. The last link in my signature line "what every 6.0 owner.." gives you a run-down of what you should be watching, why and what to watch for.
Lastly: head gaskets failure???
Best guess from here is a definite maybe. You can't tell now. You will have to do the above repairs first, then you can do a proper test of the cooling system to determine if the head gaskets have been compromised. That is a whole other chapter......