The time of morning you have mentioned she will be riding Terwilliger is a much less stressful/safer alternative, although more strenuous. I personally avoid Barbur in the early morning hours. I don't mind the high-speed commuter traffic in the mornings or evenings, but I just don't trust those out after the bars close to notice the cyclist in the bike lane. I think in those hours Barbur being low traffic is actually more risky, because tired/intoxicated drivers don't have a "pack" to follow and keep them aware of their lanes.
Although Terwilliger has much more narrow bike lanes, if you are riding in the wee hours of the morning you can take the pedestrian path almost the entire way to Barbur. Most times of day there are dog walkers and joggers using it, so the bike lanes are the way to go. But in the early morning hours it's perfectly reasonable to use the side path on your bike and much safer if you are worried about car traffic (as long as you enter the infrequent intersections cautiously, remember turning cars will not be expecting any traffic in the crosswalk) . Even though it is more of a workout, this is my preferred route late at night and in the early morning.
I'm glad you caught that crazy foot-path route google maps suggested before trying it. I blindly followed those directions late one evening and was rewarded with a brutal climb through the neighborhood up to Barbur. Those "footpaths" are quite steep and go right past people's front doors, carrying my bike up them at midnight did not seem like a good choice. From that night on I only have used the tri-met route planning tool at rtp.trimet.org