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So here's the problem. All that water is compressing world-wide air pressure to unsurvivable levels. The air is trapped and then insanely condensced between the stratosphere (is it the stratosphere I'm thinking of?) and this new 5.5 MILES taller sea level... Am I wrong, or would this not flatten Noah & his little wooden boat into splinters?

You are wrong.  But don't be sad.  This is an opportunity to learn something new!

Ambient air pressure could not crush a boat. You need a pressure differential to do that.  You see sumbarine movies or the Abyss where submarines are crushed by water pressure because the pressure outside the boat is vastly larger than the pressure inside.  Pressure x area = force.  So if you have high pressure on one side of a wall, and low pressure on the other side, the pressures are applied over the same surface area and results in a difference in force, which the walls will resist based on materials and structure.

However,   the human body - and those of many animals - evolved[1] to live within a narrow band of pressure ranges.  Bad things happen when we go outside them.  Gasses dissolve in our blood stream that do not at standard atmospheric pressure (1 atmosphere or 1 atm).  If the pressure drops before those gasses are exchanged, they can bubble out, just like carbonation in soda.  Divers know this as the bends.  But, if the decompression is slow enough, they should be fine. 

Because it's very, VERY easy to straight up die at the top of Mt. Everest for lack of oxygen.

That is because of the volume of air around the planet, not some trait inherent to Mt Everest.  IF the planet somehow had 5 miles of water dumped on it, you correctly point out that the atmosphere would also be shifted. There would be air, but it would be denser (at a higher pressure) and the atmosphere would be more shallow.

And cold. That applies to humans... I'd imagine moreso for things that require more oxygen, like big ol' Hippo lungs. And how did all the cold blooded critters survive the -20' temperatures?

Would not happen either.  Mountain tops are cold because the air pressure is lower. Not because Mt Everest is inherently cold.  As above, if the flood fills up to the top of it, then the atmosphere moves up there too.  And if you are correct that the pressure would increase, then cold is the opposite of what would happen.

When you compress gasses, they heat up proportionate to the change in volume.  It is the ideal gas law:
P is pressure, V is volume and m is mass, R is a constant and T is temperature. (Not to be confused with Mr T)
If I weren't lazy, I'd work through the equations and tell you by how much.  But it requires me dusting off calculus and physics equations I've not used in nigh 20 years.  Intuitively, I'd guess it would be a lot.  The atmosphere could be like 300 degrees F.  So staying warm would not really be the problem.  Avoiding the flash point of wood would be high on the priority list as would making sure there was enough BBQ sauce on the hippos.

Marshall Brain probably explains the basics a little better.

I hope that didn't take the sting out of your rant.
 1. or designed, if Noah were real
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