Jeff,
You probably know the threads per inch or pitch of
threads.  So 30 degrees equal 1/12 the pitch, and you
are stretching the bolt by 1/12 the thread pitch.  From
this and the length of joint, you should be able to
determine the inch/inch of stretch in the joint and
knowing the cross sectional area determine the extra
force you are applying.

Jeff,
Another dumb thought.  Do as told and then using a
torque wrench see what torque is required to start
moving the head another degree. I assume you know
the initial amount of turn to get your first reading.
I would assume that whoever set up this method was
trying to get you to take the bolt to 75 to 80 percent
of yield.  values should be close to this unless you
are bolting only statically.  Turn of the nut method
has been used successfully in many applications.
Or using a torque wrench, see what force is required
to loosen the bolt.  Sounds like fun.  If you have some
extra bolts, and your application is such that you
can use a nut on the far end, take several to yield
and see what angle was required to do this, and then
you can make a comparison.  I assume you know the
full yield value.

I don't know the formula off-hand, but I recall going through all of these calculations for my machine design class in college.  The book we used was, I think, title "Machine Design". I KNOW the authors are Schigley and Mischke, and it is one of the "classic" machine design textbooks.  Ask around if a colleague has it, or maybe go to a university library--I would certainly expect any university with a me/civ-e program to have it in their collection.  Note that friction plays a huge role in the relationship (that much I remember), so your assumption of frictional coefficient can result in a pretty big spread of your final answers.

Jeff,
I kind of agree with Bradh in that you really do not
care what the torque value is.  You really should be
interested in the clamping force that you are applying.
The turn of the nut method relies on feel to take it to
the starting point of being tight and then applying the
given turn of angle. The turn of the nut method is only
as accurate as the man with the wrench and how accurately
he can turn the nut to a given angle.  After you do determine the clamping force, you want to know what percentage of yield that you are applying to the joint.
Is this you real question?

Jeff,
To get a definative answer, you need to specify the
grade of bolt, size, pitch etc.  I know for grade 8
as an example, turning 90 degrees past the snug point
takes you into the range of 75 percent of yield.
If it were a grade 8 bolt, the same amount of turn would
yield a higher percent of yield.
What I remember as a general rule for amount of stretch
recommended for grade 8 bolts would be something like
.0034 inch per inch of bolt length being approx. equivalent
to 75 percent of yield for a fastener.
Is this a dead issue?

My first question is "Why do you want to know (the torque)?" The reason engineers specify torque + angle is that torque alone is a poor determinate of joint integrity, especially when approaching the yeild strength of the fastener, where the curve starts flattening out.  If you simply want to make sure your fastener or wrench is strong enough, great, but if you are considering specifying the final torque alone and dropping the angle, you are asking for trouble!