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I'd like to calculate the linear footage of defined beams (e.g. 2x2s, 2x4s, 2x8s, etc...) and list the total linear feet of each.

Is there a way to do this? If so, how specific can the parameters be?
Yes. I do it all the time.

Several different Fields to do it with depending if you modeled them as Walls or or Beams for one reason or another.
The specific perimeters can be reduced a little by using a good name for the Schedule. Also, layers and layer Combos can help to simplify the Criteria and Fields quite a lot. And I find the Element ID Manager to be very useful as well. In the end, what counts in the Schedule depends on who is going to use it, and for what. Sometimes adding a views of the beams and annotating the angles, miters... or other details in the Interactive Schedule is useful too. Depends on what kind of beams your scheduling.
you probably already figured it out but in case anyone else wants to know --