Like I said, I did it in less than 5 minutes, without even really knowing what the affected relations are (30 local bus routes). And the solution still sits in my local iD session waiting to be committed. Now, I grant it’s far from obvious how to do it, but then, learning intricacies of JOSM is not an easy job for a beginner either.
And I think they finally fixed that mucking-up bug. Again, on the expense of poor mappers, forcing you to download the whole relation manually if you just want to split one member. Sigh.