EGR cooler nightmare event -- always check a used one for leaks before you install...

Probably the piano wire. You used Draino, not just lye? Draino is a bit of a witch's brew, even has flakes of aluminum in it I think. I would use either Potassium Hydroxide (KOH) or Sodium Hydroxide (NaOH). Of the two, the KOH is likely easier to get (popular for soap making), more water soluble, and more effective.

More info on KOH versus NaOH

 

It's likely you poked a hole in the cooling passages with the piano wire.
You didn't say how many miles on the engine, but it might have just been timing.

It's not that difficult to replace the head gasket....

Oven cleaner and pressure washer work fast and easy and safely.
I am going to try the drain cleaner though. Just to see, and I have a spare cooler.

 

Oven cleaner isn't just NaOH anymore though is it?
Did you use a newer formulation?

 

Yeah, leakage of pressurized coolant into the EGR stream via the cooler would soon lead to disaster on two fronts---low coolant and trying to compress liquid.

I bought (but haven't yet needed to use) a used spare cooler on which one of the coolant pipes was bent. Therefore, I tested it extra carefully for leaks after cleaning it with wire and Oxi-Clean. No leak.

Music wire is harder and stonger than common sorts of cheap steel wire.

 

Oven cleaner still works....

If the cooler leaks, inside, it goes out the exhaust.... It doesn't go into the intake manifold...

 

There may be some confusion with gen 4's occasionally leaky Exhaust Heat Recovery System exchanger. If that leaks, the coolant goes out the exhaust.

If an Exhaust Gas Recirculation cooler leaks, that's gonna go into the intake.

 

It seems incredible a piano wire would bore a hole in a stainless steel egr cooler.

Stainless steel requires low rpm, high pressure drilling and lubrication. Otherwise many types of ss will heat harden.

Perhaps a drill bit was used first?

 

Or some seam was stressed, opened up?

 

The exhaust blows through the cooler, to the converter and muffler.
And the cooler is equal to and slightly lower than where the head meets the block.
It is why you had white smoke out the tail pipe. Coolant got into the EXHAUST flow.

Is coolant like a salmon and flows against the exiting exhaust?

You said you didn't lose much coolant, but if the exhaust was blocked, it created
extra pressure in the exhaust system which creates back pressure which can blow
a head gasket.

If you put the cooler in a bucket of water and put pressure through the coolant pipe, and
block the other end, you'll see bubbles if there is a leak.

If it is the cooler you purchased, the previous owner might have used sharp objects to try to
clear it, thus damaging the coolant piping. It's not really likely a piano wire will damage the
cooler. It is stainless steal, pretty tuff.

 

To be able to say that, you can only be thinking of the Exhaust Heat Recovery System exchanger. (Except the "to the converter" part; the EHRS exchanger comes after both catalytic converters, so "to the resonator and muffler" would fit better.)

The EGR cooler, which is used for Exhaust Gas Recirculation, carries exhaust gas that is being recirculated from the exhaust manifold to the intake.