Filter the skeleton / branches? find_main_branch fails

[horsto]

I feel like this is related to some work in progress: https://github.com/jni/skan/pull/214

I have these kind of images:

I want to prune the skeleton and maintain the longest axis here. The skeleton is "artificially split" by that one off branch. skimage.morphology.medial_axis fails too frequently on those data, so I thought filtering the skeleton and fusing it somehow to maintain only the one straight axis might help. But I don't know how to approach this. any ideas?