Does anyone know of any software, web site, or formula that helps
determine how long a drawbar should be for a given trailer weight,
size, and axle positions?

The correct term is 'ball mount'. There is a discussion about these
questions at:
http://www.timberman.com/RIG/trailer...omparisons.htm

Note that minimum 'ball mount' length has to be such that the tow and towed
vehicle will not collide during a maximum turn.

HTH