I would believe in God if...

[Nonpareil]

Everything you say is plausible.   I do however disagree with your statement, that irreducible complexity is complete nonsense.  

Assertions made with force, colorful adjectives, or absolutes do nothing to make them credible.  It does serve to pigeonhole one's thinking or at least their openness to dissenting opinions.

Perhaps. But I wasn't actually being hyperbolic. When I say things like "incoherent" and "nonsense concept", I actually mean something by them.

Irreducible complexity is a nonsense concept. That is, it is insufficiently well-defined, and makes use of terms that it doesn't really understand or use properly. It is incoherent. It is defined as "you can't explain this", which is not something that can be supported, as even in the best-case scenario for proponents of irreducible complexity, what they claim is unexplainable could very easily just be unexplained, and there is no means of differentiating between the two.

There is more to the issues of incoherence and nonsensical premises when it comes to irreducible complexity - I could go on for pages - but that's the basic idea. I'm not being colorful when I say that it is nonsense; I am expressing a very real issue with the formulation of the concept.

You stated the universe is demonstrably not random.  Is this correct?

Yes. The universe demonstrably follows laws and behaves in predictable, non-random ways.

The possibility of true randomness in quantum physics isn't really relevant here, before anyone brings it up. Quantum mechanics still has laws, and on any scale above that, the universe is still demonstrably not random.

If so, I am interested in your thoughts on the why and how of order.

The universe has characteristics that happen to cause it to function non-randomly. "Order" is a natural result, though the term is a bit nebulous and not necessarily appropriate in every sense here. This does not require, or imply, design.

That's about it, really.

I have seen several arguments from math wizards refuting the monkeys and typewriters argument as being theoretically impossible.

I'm not sure how or why one would do that, because the monkeys-and-typewriters thing isn't an argument. It's just an illustration of some of the properties of infinity, or other situations involving arbitrarily large sample sizes of random outputs.