I have a solution to post for future users who may encounter this problem.
I was unable to measure in edrawings. I could start the measurement tool, I could hover over the model and items would change red - but I could not click them and turn them green - which means edrawings won't display any results.
With the help of my VAR, we traced it down to the digitizer I was using. If I plugged in a mouse, it worked great, but edrawings would not recognize the left click button on my digitizer mouse. Strange - this is the only program that has ever had an issue with my hardware in over 5 years of use.
For reference, the offending digitizer is:
Wacom CTE-450 "Bamboo Fun" with the optional mouse
Driver version 5.3.3-3