Hi eggie! Thanks for the question, I am still quite new so reviews like this help me a lot.
The issue was that Organic Maps was not using these segments in biking directions, instead preferring to use the highway. This was not the case for segment 7039230 where it correctly identified the cycle path and preferred it. I reasoned that explicitly marking the ways as traversable by bike would help the navigator, but I have yet to test. You are right about the defaults, though, and it was an oversight on my part not to think about that beforehand.