Have you tried Three line tool by Chris Fullmer
Using line_normals to start a normlize line direction
clf_vertical_line_maker_loader.rb
or
Guides Axes Normal by TIG
Can add 3 guide lines normal to picked face or workplane.
clinesaxesnormal.rb
Work Plane by TIG
Adds true working plane(s) and grid(s) in your model.
WorkPlane.rb
Once you find the normal you can use the axes tool set normal to new z to force display of perpendicular inference
Like you said Gaieus "align the axes to a certain line and then use the other axis inference to draw a perpendicular one."