I'm glad we're taking this to e-mail, since it seems to have gotten a little
technical.  And by the way, hello.

1. How does direct reason differ from garden variety intuition?  Well,
garden-variety intuition is one species of direct reason, I suppose.
Just as our deductions can be known with greater or lesser degrees of
precision and certainty, so too can our direct reasonings be known
with greater or lesser degrees of precision and certainty.  And I take
"garden-variety intuition" to be that sub-group of our direct reasonings
which are known with unusually low degrees of precision and certainty.
Also, garden-variety intuition is probably less self-critical and
thoughtful than our better direct reasonings are; that is, garden-variet
intuition is probably our knee-jerk reaction, whereas something known
well through direct reason is reached after reflection and careful thought.

2. How does direct reason differ from divine revelation?  Well, I presume
that you don't believe in divine revelation, and neither do I.  Divine
revelation is supposed to be insight that you receive directly from
God or the like, which is evident to neither direct reason, indirect
reason, or observation.
But perhaps your real question is: Aren't direct reason and divine 
revelation on epistemological par, being unfounded and outrageous
claims to "knowledge" without any basis?  Well, I think that looking
at a philosopher like Aquinas will shed a little light on this.  
Basically, philosophers who believed in revelation also frequently
believed in "the natural light of reason," which is probably yet
another synonym for direct reason.  And they carefully distinguished
the two.  Things known by the natural light of reason could be known
by a noble pagan who merely used his intellect to consider the claim
in question, whereas things known by revelation could not just be figured
out.  Thus, Aquinas believed that God's existence could be known by
reason, whereas the Christian God could be known only by revelation.
Now leaving aside his questionable proofs, the interesting thing is that
even people who believed in relevation realized that some things are
known by the immediate application of reason.  They had both concepts,
but found the distinction between them clear enough.

--
But what is it that's really bugging you about direct reason? I suspect
that it is the popular but mistaken notion that everything must be
"proven."  But of course that can't be true, because first of all it
leads to an infinite regress, since you would then have to prove your
proofs, prove the proofs of your proofs, and so on.  And second of all
it is impossible because a proof only yields truth if its premises are
true, and hence on pain of circularity some premises must be known without
proof.
Or perhaps its because of the related notion that intuition is unreliable
and must be "formalized."  I see it the other way around -- formalizations
tend to falsify and oversimplify rather than lending extra clarity.  Unless
the relationship is extremely narrow to begin with.
Haven't you ever made an argument and found that another person just couldn't
"get it?"  If you clearly saw that the argument was valid, did it matter
that the other person couldn't see it?  That's what I think about direct
reason.  I see that some things are true objectively.  And if other people
don't see it, why should that shake my confidence?
           --Bryan