Is motor/gearbox with nice torque/mA numbers in the <$35 a pipe dream?
Its a pipe dream if you want to buy a high quality new motor. Its definitely doable if you spend weeks/months bargain hunting for used scrap parts and are willing to settle for less . . .
Most of those motors in the links I gave are overkill for what you want, but are only slightly overpriced. The lowest reasonable price you will ever get for a motor you describe would be $80+.
What torque is your absolute minimum required?
(if you are not sure how to calculate it, go here: http://www.societyofrobots.com/robot_arm_tutorial.shtml#joint_force
You might also want to consider using a worm gear . . . its slow, but allows you to buy a cheaper motor.
"why not use a servo."
Price.. Maybe I'm wrong. Show me some numbers.
As for servos, if they can handle the torque, use them. For what you get, they are very
affordable. Dont forget they include the price of feedback control, motor control circuitry, encoders/pots, and everything else you would otherwise need to pay for with a regular DC motor.