Getting a bottom line parallel horizontally, how does that fail? I guess I don't get it.
For me the fail would be that there is no way moving it down and get automatically inserted new start/end points so the in- & outgoing automation "levels" is the same outside the time selection.
The inspector can move selected point, and if you want to have some points parallell in their center just scale them.
If Bitwig at least activated the inspector when time-selection where made so you could adjust mean/scale/chaos like you would with selected points, it would make life somewhat easier.. and ofcourse this would need the ability to insert new point on the time selection edges.
Time selection does have split which insert new points, but that doesn't help if there already is points at start/end that you want to move down but keep the level before/after the same.