Suggest adding a snap to vertex tool. Similar to alignment line but instead of a line, a target vertex that can be set on the drawing. Click the target vertex, then shift & select rooms. Then use the Align command and enter distance. Vertices within that distance for the selected room will snap to the vertex.
An example of where it would be useful. Everything is snapped to grid of 6 inches.
I suspect you already know this based on the second image that you posted but just in case, here is how I would do it with the current available commands.
We will discuss adding a new utility to pull the points to vertices and will get back to you. I can see how it can be helpful in a scenario like the one that you shared.